ru.wikipedia.org website review
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ru.wikipedia.org is 47% geoptimaliseerd!
SEO Keyword summary for ru.wikipedia.org/wiki/%d0%9f%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f_%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle frac delta |
long Tail Keywords (2 words) delta xto xto 0frac lim delta x0displaystyle x0 fdisplaystyle f |
long Tail Keywords (3 words) delta xto 0frac lim delta xto xto 0frac delta xlim delta xto xto 0frac fxdelta x21frac 1xsqrt x21cdot x2-1frac 1xsqrt x2-1cdot |
ru.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a ru.wikipedia.org/wiki/%d0%9f%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f_%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8 page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
mdash
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
No headings were found !
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
displaystyle mathbb fcolon subset hfx ahohhrightarrow lim limits xto frac fxfx delta xfx xlim fxdelta fxx mathrm dfdxx leftfrac dydxrightvert dot leftconstrightn leftsin xrightnsinxdfrac leftarcsin xrightdfrac sqrt sinh xcosh leftxarightndfrac aanxan leftcos xrightncosxdfrac leftarccos textstyle cosh xsinh leftaxrightnaxln leftoperatorname xrightsec arctg tanh xoperatorname sch leftexrightleftnrightex ctg xrightcsc arcctg coth csch leftlog axrightndfrac xnln sec xcdot arcsec xrightfrac xsqrt xfrac xndfrac cosec xrightmathrm arccosec fin mathcal leftrightarrow exists infty oxx xxx yfxfx yfx fdelta abto bigl abbigr flxequiv sst equiv leftfnrightx fxxx ufxyz xyz partial upartial uxyfxyx xpartial yfrac fnx fix fiix fiiix fivx dnfdxnx ddot nfx fxvert overset overbrace cdot ldots textfx funderbrace xxldots textvert neq operatorname sgn cin fbfabafc fbfagbgafrac fcgc cfxlim cgx gxneq cfrac fxgx fxgxlim ffxggx leftfgrightfg yxfxgx yxlim yxdelta xyxdelta xgxdelta xfxgxdelta xfxdelta gxdelta leftfgrightfgfg fxfxdelta gxgxdelta xgx fxgxdelta gxfxgxdelta fxgxfxdelta fxfrac xgxfrac xdelta gxfrac fxgxgxfx fxgxfxgx leftcfrightcf fgrightfrac fgfgg yxfrac xgxfxgxdelta fxgxfxgxdelta fxgxfxgxfxdelta xfxfrac xgxfxfxgx fxgxfxgxg cgrightfrac cgg leftbeginmatrixxxtyytendmatrixtin leftt rightright dydxfrac dydtcdot dtdxytcdot txfrac ytxt ddxfgxfrac dfgdgcdot dgxdxfggx fgnsum ncnkfnkgk cnk yxx fxgxfxgxleftgxln gxfxfxrightforall xin dffx yfxgx ygxln yygxln gxfxfx yyleftgxln gxfxfxright yfxgxgxln xalpha alpha xxalpha ydelta xxdelta axcdot yaxdelta xaxaxadelta axlim axadelta adelta xaxcdot log axfrac acdot yxln xrightarrow xyey eyfrac sin cos ysinxdelta xsinx sinfrac cosfrac cosxfrac cosx ycosxdelta xcosx sinxfrac sinx ytgxdelta xtgxfrac sinxdelta xxcosxdelta sindelta xcosxdelta cosxdelta tgxfrac sinxcosxfrac sinxcdot cosxsinxcdot cosxcos cosxcdot sinxcos xsin xcos ctgxfrac cosxsinxfrac sinxcosxcdot sinxsin cosxsin secxfrac xsecxcdot tgx cosecxfrac xcosesxcdot ctgx arcsin sinarcsinxx cosarcsinxcdot arcsinx arcsinxfrac cosarcsinx earcsinxfrac arccos arcsinxarccosxfrac arcsinxarccosx arccosxarcsinx arccosxfrac tgarctgxx tgarctgx arctgxcdot arctgx arctgxcos arctgxfrac arctgxarcctgxfrac arctgxarcctgx arcctgxarctgx arcctgxfrac arcsecxarccosfrac arcsecxfrac arccosecxarcsecxfrac arccosecxarcsecx arccosecxfrac xleftfrac exex rightfrac exexfrac exfrac exleftfrac rightoperatorname thxfrac shxchxfrac shxcdot chxshxcdot chxch chxcdot shxch xsh xch cth cthxfrac chxshxfrac shxchxcdot shxsh chxsh schxfrac chxfrac chx cschxfrac shxfrac shx arsh arshxln arch archxln arth xbiggl biggl arcth arsech arcsch mathbf ddtmathbf tlim hto thmathbf tmathbf tfrac dmathbf tdtfrac tdt ddtftmathbf dftdtmathbf tftfrac tdtmathbf tleftfrac trightleftmathbf tdtright dxqfxfrac fqxfxq external links wikimedia foundation powered mediawiki
Mobile SEO ru.wikipedia.org/wiki/%d0%9f%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f_%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for ru.wikipedia.org/wiki/%d0%9f%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f_%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
No contextual keywords found in path
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
creativecommons.org creative commons cc bysa
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ru.m.wikipedia.org |
w httpsruwikipediaorgwindexphptitleoldid137374742
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wiki /%D0%9F%D1%80%D0%B5%D0%B4%D0%B5%D0%BB_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)
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wikimediafoundation.org wikimedia foundation inc
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Links to external pages
Outloing links
resh.edu.ru
www.planetcalc.ru
www.zero2hero.org
mathworld.wolfram.com
wikidata-externalid-url.toolforge.org
www.bigenc.ru
www.krugosvet.ru
www.larousse.fr
www.encyclopediaofmath.org
www.britannica.com
www.sapere.it
encyklopedia.pwn.pl
www.treccani.it
www.d-nb.info
olduli.nli.org.il
id.ndl.go.jp
aleph.nkp.cz
www.wikidata.org
af.wikipedia.org
am.wikipedia.org
an.wikipedia.org
ar.wikipedia.org
az.wikipedia.org
azb.wikipedia.org
ba.wikipedia.org
bn.wikipedia.org
bs.wikipedia.org
ca.wikipedia.org
ckb.wikipedia.org
cs.wikipedia.org
cv.wikipedia.org
de.wikipedia.org
el.wikipedia.org
en.wikipedia.org
eo.wikipedia.org
es.wikipedia.org
et.wikipedia.org
eu.wikipedia.org
fa.wikipedia.org
fi.wikipedia.org
fr.wikipedia.org
fur.wikipedia.org
ga.wikipedia.org
gl.wikipedia.org
he.wikipedia.org
hi.wikipedia.org
hr.wikipedia.org
hu.wikipedia.org
hy.wikipedia.org
id.wikipedia.org
io.wikipedia.org
is.wikipedia.org
it.wikipedia.org
ja.wikipedia.org
ka.wikipedia.org
ko.wikipedia.org
la.wikipedia.org
lmo.wikipedia.org
lo.wikipedia.org
lt.wikipedia.org
lv.wikipedia.org
mk.wikipedia.org
ml.wikipedia.org
mr.wikipedia.org
ms.wikipedia.org
mt.wikipedia.org
my.wikipedia.org
nn.wikipedia.org
no.wikipedia.org
oc.wikipedia.org
om.wikipedia.org
pl.wikipedia.org
pnb.wikipedia.org
pt.wikipedia.org
ro.wikipedia.org
scn.wikipedia.org
sco.wikipedia.org
sh.wikipedia.org
simple.wikipedia.org
sk.wikipedia.org
sl.wikipedia.org
sq.wikipedia.org
sr.wikipedia.org
sv.wikipedia.org
szl.wikipedia.org
ta.wikipedia.org
tr.wikipedia.org
tt.wikipedia.org
ur.wikipedia.org
uz.wikipedia.org
vec.wikipedia.org
vi.wikipedia.org
wa.wikipedia.org
wuu.wikipedia.org
yi.wikipedia.org
zh-classical.wikipedia.org
zh-yue.wikipedia.org
www.wikidata.org
foundation.wikimedia.org
developer.wikimedia.org
foundation.wikimedia.org
www.wikimediafoundation.org
SEO Advice for ru.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 0% | A title should reflect the contents of a site. This site has a 0 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 65 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 50% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 177 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 5 level 1 folders and 8 folders above or in the first level of navigation. | |
Headings | 0% | Headers should reflect the contents of a site. This site has a 0 % match | |
Links | 0% | Link anchors should to some degree reflect the contents of a site. This site has a 0 % match | |
Image alt tags | 25% | Image alt tags should to some degree reflect the contents of a site. This site has a 9 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 99% | 98.888888888889 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 5739 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 85.03% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 20% | There are no important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 822 inline style declarations ( <a style="color:green">) with a size of 26910 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (4) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 100% | Perfect, we found a correct use of normalized headings ! |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
ru.wikipedia.org images and descriptions
303 images found at ru.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/derivative_of_a_function.svg/200px-derivative_of_a_function.svg.png height: 190 width: 200 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4efa9cde595361b1ea89743b7080654c3c8614f7 height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}\in \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/59e21b4a7832b51c744147f231adab3052656351 height: height attribute not set width: width attribute not set description: {\displaystyle f\colon u(x_{0})\subset \mathbb {r} \to \mathbb {r} .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ecc510a8d563325ae69bacea7ec699728939269 height: height attribute not set width: width attribute not set description: {\displaystyle u(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67bdc4138563d1d1f9899fe343a62a1d359d1164 height: height attribute not set width: width attribute not set description: {\displaystyle f(x_{0}+h)=f(x_{0})+ah+o(h),h\rightarrow 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61 height: height attribute not set width: width attribute not set description: {\displaystyle f} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/86f21d0e31751534cd6584264ecf864a6aa792cf height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/13a06f7785c58695a08e984db6acbfddc0adefaa height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})=\lim \limits _{x\to x_{0}}{\frac {f(x)-f(x_{0})}{x-x_{0}}}=\lim _{\delta x\to 0}{\frac {f(x_{0}+\delta x)-f(x_{0})}{\delta x}}=\lim \limits _{{\delta x}\to 0}{\frac {\delta {f(x)}}{\delta x}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2978351defe6cb812b175c2e8ded14fa67f6bbbd height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})=f'_{x}(x_{0})=\mathrm {d} \!f(x_{0})={\frac {df}{dx}}(x_{0})=\left.{\frac {dy}{dx}}\right\vert _{x=x_{0}}={\dot {y}}(x_{0}).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fc0504631d67f739ac0497127d0f8c527492fa72 height: height attribute not set width: width attribute not set description: {\displaystyle \left(const\right)^{(n)}=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f17a3aa8240f05b781200c3abe03ae38d010a3db height: height attribute not set width: width attribute not set description: {\displaystyle \left(\sin x\right)^{(n)}=\sin(x+{\dfrac {\pi n}{2}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8630f95b6abf30a9135f866da4885e69fb863a9a height: height attribute not set width: width attribute not set description: {\displaystyle \left(\arcsin x\right)'={\dfrac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3dd3ed63c4f1073c96522699a05a01be2a3076f height: height attribute not set width: width attribute not set description: {\displaystyle (\sinh x)'=\cosh x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2fc1c97640d8951d50c4fa4178040c91d8d5096c height: height attribute not set width: width attribute not set description: {\displaystyle \left(x^{a}\right)^{(n)}={\dfrac {a!}{(a-n)!}}x^{a-n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed19de5b2557477279558d4d3239a08369f932d height: height attribute not set width: width attribute not set description: {\displaystyle \left(\cos x\right)^{(n)}=\cos(x+{\dfrac {\pi n}{2}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d13d08cd05ccb372123bcfbdb54442683ab4e215 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\arccos x\right)'=-{\dfrac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f641fc840b64e34402352b091e1239908c1c0d58 height: height attribute not set width: width attribute not set description: {\textstyle (\cosh x)'=\sinh x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45e6efb400343cbe3bfca7d12bcf89d8fe400203 height: height attribute not set width: width attribute not set description: {\displaystyle \left(a^{x}\right)^{(n)}=a^{x}\ln ^{n}a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c05e60613f96ab5a1588aea88e49dc50c09b5f height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {tg} x\right)'=\sec ^{2}x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f7fb9d6da211dd1deb9e9333fa22f811968bbec height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {arctg} x\right)'={\dfrac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6db0872f0d958181d8d199f29ee9432588a16498 height: height attribute not set width: width attribute not set description: {\displaystyle (\tanh x)'=\operatorname {sch} ^{2}x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bfeadbb9ddbe46d76048445757d1298702d32f9f height: height attribute not set width: width attribute not set description: {\displaystyle \left(e^{x}\right)^{\left(n\right)}=e^{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4306f35dede4c703a41e196a0c71ce1dc4aad1f1 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {ctg} x\right)'=-\csc ^{2}x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e45742a8cecb9024ca6de18dbff55b0377855aa0 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {arcctg} x\right)'=-{\dfrac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/39b39a78bd11ae4c5dd163d7d9738e1df0225689 height: height attribute not set width: width attribute not set description: {\displaystyle (\coth x)'=-\operatorname {csch} ^{2}x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/daf291b02e34bb48bd479632003abf5e356f0719 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\log _{a}x\right)^{(n)}={\dfrac {(-1)^{n-1}(n-1)!}{x^{n}\ln a}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/abc943f9f355e2201154b0723fc4be644c6c17f2 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {sec} x\right)'=\sec x\cdot \mathrm {tg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5b5619225f331a1be7ea6fd26a814bc11c66037e height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {arcsec} x\right)'={\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e9c2b5b3d9316f03ebd91250fc0415d0d6bb589 height: height attribute not set width: width attribute not set description: {\displaystyle (\mathrm {sch} \ x)'=-{\frac {\sinh x}{\cosh ^{2}x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a825aa46edcb3bcb68954d24b7464bae495088b5 height: height attribute not set width: width attribute not set description: {\displaystyle (\ln {x})^{(n)}={\dfrac {(-1)^{n-1}(n-1)!}{x^{n}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e61eeb61db5709cf1444ea6e480588eef387fb0f height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {cosec} x\right)'=-\mathrm {cosec} \ x\cdot \mathrm {ctg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7251b4a33012ce1ec25a9774bb44981d8941d428 height: height attribute not set width: width attribute not set description: {\displaystyle \left(\operatorname {arccosec} x\right)'=-{\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a99f5af31ca707b00726655b394fb2ab39fddc72 height: height attribute not set width: width attribute not set description: {\displaystyle (\mathrm {csch} \ x)'=-{\frac {\cosh x}{\sinh ^{2}x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc15f7bc4034ace9faccf92eb8e3f245541c5e6e height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91353961c46423756a7dae63379cd00c59202e07 height: height attribute not set width: width attribute not set description: {\displaystyle f\in {\mathcal {d}}(x_{0})\leftrightarrow \exists f'(x_{0})\in (-\infty ;\infty ).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8f11dcc72497100b61ab9b99d828ffee79bd374 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=f(x_{0})+f'(x_{0})(x-x_{0})+o(x-x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10dc989c85f4995ca0c67ec4e7f737763b057165 height: height attribute not set width: width attribute not set description: {\displaystyle x\to x_{0}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e98906ac9114317f92338a895b5057127ad8095f height: height attribute not set width: width attribute not set description: {\displaystyle \delta x=x-x_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/941faf97bfce9388ede28241c4e767e69d965c74 height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=f(x)-f(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/adbac99e343fcb075238e12224d08939ea6451ae height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=f(x_{0}+\delta x)-f(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ec756993d89cc1bd74f84040c07f5e11f0a8102 height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d7623227a4d7f2305a0e41c37f0c3357c9e8b9ca height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})=\lim \limits _{\delta x\to 0}{\frac {\delta f}{\delta x}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a6be90b157a47318b0043b84bb712295e8a03107 height: height attribute not set width: width attribute not set description: {\displaystyle f\colon (a,b)\to \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4a5ad1604e62cdd5f0c6b99f257459a0ad89a0 height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}\in (a,b).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/afdcfc474e70e3c7a191fda6632a41a11ccb869b height: height attribute not set width: width attribute not set description: {\displaystyle f'\colon (a,b)\to \mathbb {r} .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f022c627220e819571ac3e7120b31b84ca5e79a0 height: height attribute not set width: width attribute not set description: {\displaystyle f\in c^{(1)}{\bigl (}(a,b){\bigr )}.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/derivative-svg.svg/300px-derivative-svg.svg.png height: 280 width: 300 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/11088953a3161d6f349ba57e5e54aa69e9c06214 height: height attribute not set width: width attribute not set description: {\displaystyle f\colon u(x_{0})\to \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b35dd572e629881da4083ad1681bc7cf420304 height: height attribute not set width: width attribute not set description: {\displaystyle x_{0},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4c19500648f3bc3fa14e8bd7a645eab77dd63d6b height: height attribute not set width: width attribute not set description: {\displaystyle f_{l}(x)\equiv f(x_{0})+f'(x_{0})(x-x_{0}).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d0f63e0d5ebca136b8b6202eba076bac83b5c05 height: height attribute not set width: width attribute not set description: {\displaystyle f_{l}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14acdab8bb33a0931f9679f477e7491010e1698a height: height attribute not set width: width attribute not set description: {\displaystyle s=s(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d2975f35d58c327e643a6548b026646bb174b75 height: height attribute not set width: width attribute not set description: {\displaystyle v(t_{0})=s'(t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a height: height attribute not set width: width attribute not set description: {\displaystyle t_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e9fbde1038511c9270c270eb6aa61af29db613e5 height: height attribute not set width: width attribute not set description: {\displaystyle s'(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7a98ca10fbf932ed01f1c662e809335e89d44a9e height: height attribute not set width: width attribute not set description: {\displaystyle s''(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67d385527afd6f54df94bed874f98ad258bdda0d height: height attribute not set width: width attribute not set description: {\displaystyle a(t_{0})=s''(t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ff3177424727fe9cbac5e6249bbd59cef6c1152 height: height attribute not set width: width attribute not set description: {\displaystyle t_{0}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2311a6a75c54b0ea085a381ba472c31d59321514 height: height attribute not set width: width attribute not set description: {\displaystyle y=f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ea153ca7e4a53e290c347ab731724265f98c0b60 height: height attribute not set width: width attribute not set description: {\displaystyle y=f(x).} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/what_is_derivative_%28animation%29.gif/220px-what_is_derivative_%28animation%29.gif height: 234 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3be43d9f6711bcdcee6db87b730e63e6f2734e5d height: height attribute not set width: width attribute not set description: {\displaystyle f^{(0)}(x_{0})\equiv f(x_{0}).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e89738f5135d781f648f75d9e7e58695eff71762 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(1)}(x_{0})\equiv f'(x_{0}).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9dfb1963ccde0e87eb3838f51dc19041e2ff3816 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(n)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9cb88690b4d799f356719fd18b835cceb398af54 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(n+1)}(x_{0})=\left(f^{(n)}\right)'(x_{0}).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/96b9c7952b88abb2880e9b70945b74f683eeb869 height: height attribute not set width: width attribute not set description: {\displaystyle f''(x_{0})=(f'(x))'|_{x=x_{0}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1da18dc4b84623c43defaf5a181dcdae46db3d97 height: height attribute not set width: width attribute not set description: {\displaystyle u=f(x,y,z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d08d690d7e19ea7aee8574fc6abd6a15d97fa026 height: height attribute not set width: width attribute not set description: {\displaystyle x,y,z,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/39177ddeeb9f9a393b664e522bc8e3bf0face153 height: height attribute not set width: width attribute not set description: {\displaystyle (x_{0},y_{0},z_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f3f95a45c367af846231cc432941df1e719c13ac height: height attribute not set width: width attribute not set description: {\displaystyle u''_{x^{2}}=f''_{x^{2}}(x_{0},y_{0},z_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ec5ad52a28936140c7286d0b3f84914af55f5496 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial ^{2}u}{\partial x^{2}}}={\frac {\partial ^{2}f(x_{0},y_{0},z_{0})}{\partial x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/270dd227c42d4481b62cb19ed38c756e845567d9 height: height attribute not set width: width attribute not set description: {\displaystyle u''_{xy}=f''_{xy}(x_{0},y_{0},z_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43d0286ddb4d5e7188fb286aab597c5f9e83ac2e height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial ^{2}u}{\partial x\partial y}}={\frac {\partial ^{2}f(x_{0},y_{0},z_{0})}{\partial x\partial y}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04f53da8d7d86152845dc7ce75a01140f9ff0f07 height: height attribute not set width: width attribute not set description: {\displaystyle c^{(n)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac1b7d6e1a488c73c3acab969be7c4a8f2a10aa height: height attribute not set width: width attribute not set description: {\displaystyle f^{(n)}(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/90eb233e6e50a123c4cdb28b90512e7b1659c655 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(1)}(x_{0})=f'(x_{0})=f^{i}(x_{0}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e9b719e7b71c7cb5e2cf5e09a3548d6c2c2c40b height: height attribute not set width: width attribute not set description: {\displaystyle f^{(2)}(x_{0})=f''(x_{0})=f^{ii}(x_{0}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e60ea8429e310eef84fad50e25713f916eb8c1ec height: height attribute not set width: width attribute not set description: {\displaystyle f^{(3)}(x_{0})=f'''(x_{0})=f^{iii}(x_{0}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08360d3e18143011670b96e431ce2553aea76538 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(4)}(x_{0})=f^{iv}(x_{0}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/169aa26c3b0a6097d6eeac3cbb23fe80890aac48 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d^{n}\!f}{dx^{n}}}(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fc48556f6bc82b7dd72f6a8518b6f2646af01339 height: height attribute not set width: width attribute not set description: {\displaystyle {\dot {x}}(t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560 height: height attribute not set width: width attribute not set description: {\displaystyle t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/be6d7492e2d48bf34fdd5dffa189b188c140820c height: height attribute not set width: width attribute not set description: {\displaystyle t=t_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/392b3b69fb0bcac125f437c4df10f04462dcf0dd height: height attribute not set width: width attribute not set description: {\displaystyle {\ddot {f}}(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a8e60f16276c7e92f7277dddb00904de742e7ce9 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {d} ^{n}\!f(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/914df42c27438c724a590ee2c631152a35a9a54c height: height attribute not set width: width attribute not set description: {\displaystyle \partial ^{n}\!f(x_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb36605624ab2287dc5ec558513c625b88acfee3 height: height attribute not set width: width attribute not set description: {\displaystyle f_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8daf48189eff682d0d5f6b2ab9cd78e2209a72e height: height attribute not set width: width attribute not set description: {\displaystyle f_{xx}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c1d122c8d6468eff6631b7173e553aa9c6e6904d height: height attribute not set width: width attribute not set description: {\displaystyle f_{x}\vert _{x=x_{0}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c38dcb92c3f7d8404404bb7995b8e90d85949b01 height: height attribute not set width: width attribute not set description: {\displaystyle f^{(n)}(x_{0})={\frac {d^{n}\!f}{dx^{n}}}(x_{0})={\overset {\overbrace {\cdot \cdot \ldots \cdot } ^{n\ {\text{раз}}}}{f}}(x_{0})=\mathrm {d} ^{n}\!f(x_{0})=f{\underbrace {_{xx\ldots x}} _{n\ {\text{раз}}}}\vert _{x=x_{0}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84ddac4ae10b1aa4a11741c79771a583419fb1fb height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=x^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/424863a8c6b2dc57ca4e6cd9b27afd136f3b4f1a height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})=\lim \limits _{x\to x_{0}}{\frac {x^{2}-x_{0}^{2}}{x-x_{0}}}=\lim \limits _{x\to x_{0}}{\frac {(x-x_{0})(x+x_{0})}{x-x_{0}}}=\lim \limits _{x\to x_{0}}(x+x_{0})=2x_{0}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/094ddc9667a7f47e36687c1d2a94d35c0c7d5c67 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=|x|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/665c0f32aaecad604c83659ab88da6d4e4f26a6d height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}\neq 0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c205e0a9270f67e9f55595d2eaa753fb70daa4e4 height: height attribute not set width: width attribute not set description: {\displaystyle f'(x_{0})=\operatorname {sgn} x_{0},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ec838dfd8a4a659b2877f93a6b53f22fc7777d07 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {sgn} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a72c7ee7f5880074db8a515f79734b09160980b8 height: height attribute not set width: width attribute not set description: {\displaystyle x_{0}=0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84b40d3731603e9e518bb9fb5a16a14a1f729ccd height: height attribute not set width: width attribute not set description: {\displaystyle f'_{+}(x_{0})=1,\;f'_{-}(x_{0})=-1,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25b6ab1762925585cd7605809caa8b1b5284177b height: height attribute not set width: width attribute not set description: {\displaystyle f,g} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935 height: height attribute not set width: width attribute not set description: {\displaystyle [a,b]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c height: height attribute not set width: width attribute not set description: {\displaystyle (a,b)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455 height: height attribute not set width: width attribute not set description: {\displaystyle c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/151d6d9bd64c4cd7e2010fb08ef6bc4e7c56e97b height: height attribute not set width: width attribute not set description: {\displaystyle f'(c)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f84ce11adae917b3d5f813729260a28227d0e83b height: height attribute not set width: width attribute not set description: {\displaystyle f'(c)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2cb3eb21e944c077ddbb69a60969d47141f02c height: height attribute not set width: width attribute not set description: {\displaystyle c\in (a,b)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e8e47493a1c07af5408a7aed855929fd2460fff height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {f(b)-f(a)}{b-a}}=f'(c)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e7a53c0df5d85b36e3fd327c74db998f679f4f55 height: height attribute not set width: width attribute not set description: {\displaystyle g'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/232da8aa32894ed493c5f63de50b5c060b42a9ba height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {f(b)-f(a)}{g(b)-g(a)}}={\frac {f'(c)}{g'(c)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64d2a00e42a2863fb785962ff464c84f16b600ab height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21 height: height attribute not set width: width attribute not set description: {\displaystyle \infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f022fde7dae42ed7a4bf38125e329293ac4d5ce5 height: height attribute not set width: width attribute not set description: {\displaystyle g'(x)\neq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9186ac40d31fd1b92d69283a5a91702a30dbc034 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to c}{\frac {f'(x)}{g'(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f654e25c3bbbbb7825d619fd3526371fe1cb65b2 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029 height: height attribute not set width: width attribute not set description: {\displaystyle c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/329cd3f5ad2dbfc8efa3629d59cf4a49fc76c6f7 height: height attribute not set width: width attribute not set description: {\displaystyle f=f(x),g=g(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/451ab552f1d46f6cd1fd857d66e738cdc23357d6 height: height attribute not set width: width attribute not set description: {\displaystyle c'=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/538bdb4c4940b4ded5c7f64a8cd8fb8174d21f9a height: height attribute not set width: width attribute not set description: {\displaystyle x'=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c3a92e1432b7e1f04ab2067544126ae6d8866889 height: height attribute not set width: width attribute not set description: {\displaystyle \left(f+g\right)'=f'+g'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/42772379fcc0c6bb11dd4d279babe6e4b00be760 height: height attribute not set width: width attribute not set description: {\displaystyle y(x)=f(x)+g(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac6f6cd7d782cec113f83f2aa79e1ebb9c8c3c3 height: height attribute not set width: width attribute not set description: {\displaystyle y'(x)=\lim _{\delta x\to 0}{\frac {y(x+\delta {x})-y(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/97e6e60e568b4a503320cfa1fe113124e71286ff height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {(f(x+\delta {x})+g(x+\delta {x}))-(f(x)+g(x))}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af91f10740587280aa94a55565b5887d890bde8a height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{({\frac {f(x+\delta x)-f(x)}{\delta x}}+{\frac {g(x+\delta x)-g(x)}{\delta x}})}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f906ae75d8ff9740c267b1f119753b533aa7efc1 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {f(x+\delta x)-f(x)}{\delta x}}+\lim _{\delta x\to 0}{\frac {g(x+\delta x)-g(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6610e2c63357814d76385f5d5b813fd219051b01 height: height attribute not set width: width attribute not set description: {\displaystyle =f'(x)+g'(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e7bc05b7892076e90867f0dbdabe345dfc8c4291 height: height attribute not set width: width attribute not set description: {\displaystyle \left(fg\right)'=f'g+fg'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/34b9ac5a2b871e57a18548f1376ec3f797186b41 height: height attribute not set width: width attribute not set description: {\displaystyle y(x)=f(x)g(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/19f68b9136c25f2a2a943f9da1e743e511ec203d height: height attribute not set width: width attribute not set description: {\displaystyle \delta f(x)=f(x+\delta x)-f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7029b400f1d727d68b956982d7d7923ae1aad043 height: height attribute not set width: width attribute not set description: {\displaystyle \delta g(x)=g(x+\delta x)-g(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ae5232504d50953d16cafafa9895f3ec0234afc height: height attribute not set width: width attribute not set description: {\displaystyle y'(x)=\lim _{\delta x\to 0}{\frac {y(x+\delta x)-y(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28909cb0a425fed63a748133ef6614d2b316f1af height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {f(x+\delta x)g(x+\delta x)-f(x)g(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4989a13cd66ae761fd91b868f7e6029d1f140b4 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {(f(x)+\delta f(x))(g(x)+\delta g(x))-f(x)g(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/384030a106df3c9889784fc44cca4a1851615c72 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {f(x)g(x)+f(x)\delta g(x)+\delta f(x)g(x)+\delta f(x)\delta g(x)-f(x)g(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2eaf4d31f66fc95a8b26ff58ea37884fe7d2953f height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}(f(x){\frac {\delta g(x)}{\delta x}}+g(x){\frac {\delta f(x)}{\delta x}}+\delta g(x){\frac {\delta f(x)}{\delta x}})=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09d696527ded63116ee686f417ea75c760ef34f1 height: height attribute not set width: width attribute not set description: {\displaystyle =f(x)g'(x)+g(x)f'(x)+0f'(x)=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/559a924e2e27efcb235b4679836c91b04607061a height: height attribute not set width: width attribute not set description: {\displaystyle =f'(x)g(x)+f(x)g'(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ed5720d013ebd2f82446bd5250d9c224e2d5ff0e height: height attribute not set width: width attribute not set description: {\displaystyle \left(cf\right)'=cf'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/320d75a68534beaf54f199f443b0672462674169 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {f}{g}}\right)'={\frac {f'g-fg'}{g^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2943f31df96ce10306933d264abe22a4f0454ab5 height: height attribute not set width: width attribute not set description: {\displaystyle y(x)={\frac {f(x)}{g(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84eb1900c437ed6f2813bc00ca346edf6ae33f21 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {{\frac {f(x+\delta x)}{g(x+\delta x)}}-{\frac {f(x)}{g(x)}}}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9f901d0834e1e5274dad9ebb0850a3ddbb261022 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {f(x+\delta x)g(x)-f(x)g(x+\delta x)}{g(x+\delta x)g(x)\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0391342c3ae1dcb669949cd0cb3a3fb74784052b height: height attribute not set width: width attribute not set description: {\displaystyle ={\frac {1}{g^{2}(x)}}\lim _{\delta x\to 0}{\frac {(f(x)+\delta f(x))g(x)-f(x)(g(x)+\delta g(x))}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f04e63b313ca20ac6b567ad07a9451d4fd220c9 height: height attribute not set width: width attribute not set description: {\displaystyle ={\frac {1}{g^{2}(x)}}\lim _{\delta x\to 0}{\frac {f(x)g(x)+\delta f(x)g(x)-f(x)g(x)-f(x)\delta g(x)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a26009fe2cb953e6fb078000cabdb455c32008a height: height attribute not set width: width attribute not set description: {\displaystyle ={\frac {1}{g^{2}(x)}}\lim _{\delta x\to 0}{(g(x){\frac {\delta f(x)}{\delta x}}-f(x){\frac {\delta g(x)}{\delta x}})}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6743d638398dcab7df411b9d6c77de79e7684131 height: height attribute not set width: width attribute not set description: {\displaystyle ={\frac {1}{g^{2}(x)}}(g(x)f'(x)-f(x)g'(x))=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67ec89f9d1dd9a715a77dbbb929048dc9bcc39b7 height: height attribute not set width: width attribute not set description: {\displaystyle ={\frac {f'(x)g(x)-f(x)g'(x)}{g^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2017cf0dfa325ae502194b818e58167766a1f248 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {c}{g}}\right)'=-{\frac {cg'}{g^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66c1512a040f80645b424f10cb2fc237be942c83 height: height attribute not set width: width attribute not set description: {\displaystyle \left\{{\begin{matrix}x=x(t),\\y=y(t),\end{matrix}}\;\;t\in \left[t_{1};t_{2}\right]\right.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b03d3048510961395d3e762c5a6fda64d2ee43d2 height: height attribute not set width: width attribute not set description: {\displaystyle y'_{x}={\frac {dy}{dx}}={\frac {dy}{dt}}\cdot {\frac {dt}{dx}}=y'_{t}\cdot t'_{x}={\frac {y'_{t}}{x'_{t}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7e6f9f8375f2a215727d67f07d3a2c7a5a47dc75 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dx}}f(g(x))={\frac {df(g)}{dg}}\cdot {\frac {dg(x)}{dx}}=f'_{g}g'_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a23f91f76f92bfe830c99300f6e88c9f0aaf5f21 height: height attribute not set width: width attribute not set description: {\displaystyle (fg)^{(n)}=\sum \limits _{k=0}^{n}{c_{n}^{k}f^{(n-k)}g^{(k)}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b088b67f00e4739e57c658ac7dd5913898013ac height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6610819ec7d3b3f0ad716711ad3af7204cf8320d height: height attribute not set width: width attribute not set description: {\displaystyle y(x)=|x|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01 height: height attribute not set width: width attribute not set description: {\displaystyle [-1,1]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99d0a1b41cfebaf9ce720ec45fa5b14361711d43 height: height attribute not set width: width attribute not set description: {\displaystyle f'(x)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/df2bce36ba50385e1b2acffb8320bca1a7675ca7 height: height attribute not set width: width attribute not set description: {\displaystyle (f(x)^{g(x)})'=f(x)^{g(x)}\left(g'(x)\ln f(x)+{\frac {g(x)f'(x)}{f(x)}}\right)(\forall x\in d_{f}:f(x)>0)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb472db1c33b8779ef8d9ff74d29be1ea43ecec5 height: height attribute not set width: width attribute not set description: {\displaystyle y=f(x)^{g(x)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/485c1c8816db68ddf9e9ff803b4f4fc5c8d7736f height: height attribute not set width: width attribute not set description: {\displaystyle \ln y=g(x)\ln f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f83f9f10f4d3ba37b24f27c299b067a31133c856 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {y'}{y}}=g'(x)\ln f(x)+{\frac {g(x)f'(x)}{f(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61d1c73c16d6b2fe66d0356a3aaace6717e5b2ff height: height attribute not set width: width attribute not set description: {\displaystyle y'=y\left(g'(x)\ln f(x)+{\frac {g(x)f'(x)}{f(x)}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/da843eb5b1ceccc1cfe24f9859d685f950ea1e2b height: height attribute not set width: width attribute not set description: {\displaystyle y'=f(x)^{g(x)}(g'(x)\ln f(x)+{\frac {g(x)f'(x)}{f(x)}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d0cd7d7c75340e779d82658e19d1720ce84ab127 height: height attribute not set width: width attribute not set description: {\displaystyle f'(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c7ecb06c51aa5eb67cb4363751c8774977ba3cd5 height: height attribute not set width: width attribute not set description: {\displaystyle x^{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75692bf7424b74c54189146669955fcda0b36527 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha \cdot x^{\alpha -1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e966416292d99a815d090e0c88c0039b668d1a14 height: height attribute not set width: width attribute not set description: {\displaystyle x\in \mathbb {d} (f)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70 height: height attribute not set width: width attribute not set description: {\displaystyle \delta x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/32f42988e66f4c581c38fc1d13e239f4cb061a83 height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=(x+\delta x)^{\alpha }-x^{\alpha }=x^{\alpha }((1+{\frac {\delta x}{x}})^{\alpha }-1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1e166700a4848ad5ec7ee1c20c6a6f0ee577e36 height: height attribute not set width: width attribute not set description: {\displaystyle (x^{\alpha })'=\lim _{\delta x\to 0}{\frac {\delta y}{\delta x}}=\lim _{\delta x\to 0}{\frac {x^{\alpha }((1+{\frac {\delta x}{x}})^{\alpha }-1)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a69bf9a326a5651f58a4c87d75e4bc91372f4d5 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {\alpha \cdot x^{\alpha }\cdot {\frac {\delta x}{x}}}{\delta x}}=\alpha \cdot x^{\alpha -1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c031175c5142c25946f910813bf41c034fed75c1 height: height attribute not set width: width attribute not set description: {\displaystyle a^{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8454bf4900f30c0783d42deca3069590449a40b3 height: height attribute not set width: width attribute not set description: {\displaystyle a^{x}\cdot \ln {a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b2a3de0960fc828265d7150674ece5c51578609b height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=a^{x+\delta x}-a^{x}=a^{x}(a^{\delta x}-1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2571f36831b4638d9d94cd095949a7bbbcb100c2 height: height attribute not set width: width attribute not set description: {\displaystyle (a^{x})'=\lim _{\delta x\to 0}{\frac {\delta y}{\delta x}}=\lim _{\delta x\to 0}{\frac {a^{x}(a^{\delta x}-1)}{\delta x}}=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65bd8b67437a1ef729c26a41d07f41b93f65d013 height: height attribute not set width: width attribute not set description: {\displaystyle =\lim _{\delta x\to 0}{\frac {a^{x}\cdot \delta x\cdot \ln {a}}{\delta x}}=a^{x}\cdot \ln {a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0f84c35dc3a8690dc5fc440e1dd117d043dc54e3 height: height attribute not set width: width attribute not set description: {\displaystyle \log _{a}{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23ae10359e1352a3a2bedbbf7296d7328f8ffc51 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{x\cdot \ln {a}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5436b58722af8edff1ef3ccd9932c7b57fbd5aa8 height: height attribute not set width: width attribute not set description: {\displaystyle (\log _{a}x)'={\frac {1}{\ln {a}}}\cdot (\ln {x})'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68c47eeb7700e9adf786e4f4db84a6911c9a3b8a height: height attribute not set width: width attribute not set description: {\displaystyle \ln {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/193b8b2617ec802d9f0b67f8689079a03aff4e56 height: height attribute not set width: width attribute not set description: {\displaystyle y_{x}=\ln {x}\rightarrow x_{y}=e^{y},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cb20b4219154bd70af90892447419d4cbd76f7e4 height: height attribute not set width: width attribute not set description: {\displaystyle y_{x}'=(\ln {x})'={\frac {1}{(e^{y})'}}={\frac {1}{e^{y}}}={\frac {1}{x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/30d78f1c6bb9fb6fdd64103b00c01a5a85a9d226 height: height attribute not set width: width attribute not set description: {\displaystyle (\log _{a}{x})'={\frac {1}{x\cdot \ln {a}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09b4b55580d6a821a07ad9fe35be88976917b10b height: height attribute not set width: width attribute not set description: {\displaystyle \sin x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/184ba70c3a71df25a25c09f34cd7f8175a9b5280 height: height attribute not set width: width attribute not set description: {\displaystyle \cos x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/85ed2b88b7bfb3116461d78b3bf54417215aa4bc height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=sin(x+\delta x)-sin(x)=2sin({\frac {x+\delta x-x}{2}})\cdot cos({\frac {x+\delta +x}{2}})=2sin({\frac {\delta x}{2}})\cdot cos(x+{\frac {\delta x}{2}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0618d0b68751cd1744ec0c6253dd2c4979504ad3 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{\delta x\to 0}{\frac {\delta y}{\delta x}}=\lim _{\delta x\to 0}{\frac {2sin({\frac {\delta x}{2}})\cdot cos(x+{\frac {\delta x}{2}})}{\delta x}}=\lim _{\delta x\to 0}{\frac {sin({\frac {\delta x}{2}})\cdot cos(x+{\frac {\delta x}{2}})}{\frac {\delta x}{2}}}=\lim _{\delta x\to 0}{\frac {sin({\frac {\delta x}{2}})}{\frac {\delta x}{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99591e3cfd0ce9363e14f7ecfad9e39b33aefcc3 height: height attribute not set width: width attribute not set description: {\displaystyle \cdot \lim _{\delta x\to 0}{cos(x+{\frac {\delta x}{2}})}=cos(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/506006811ed806ee55fb1db8a7c1060c012fa313 height: height attribute not set width: width attribute not set description: {\displaystyle -\sin x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b197c39a46b2a4eae15d899bed305435dd5c1ee3 height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=cos(x+\delta x)-cos(x)=-2sin({\frac {x+\delta x+x}{2}})\cdot sin({\frac {x+\delta -x}{2}})=-2sin(x+{\frac {\delta x}{2}})\cdot sin({\frac {\delta x}{2}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ff0795e883995cbd7a8ff293ce974c7dfaaa7b7 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{\delta x\to 0}{\frac {\delta y}{\delta x}}=\lim _{\delta \to 0}{\frac {-2sin(x+{\frac {\delta x}{2}})\cdot sin({\frac {\delta x}{2}})}{\delta x}}=\lim _{\delta \to 0}{\frac {-sin(x+{\frac {\delta x}{2}})\cdot sin({\frac {\delta x}{2}})}{\frac {\delta x}{2}}}=\lim _{\delta x\to 0}{\frac {sin({\frac {\delta x}{2}})}{\frac {\delta x}{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d139eaebaf71f63984985613106d72751276f954 height: height attribute not set width: width attribute not set description: {\displaystyle \cdot \lim _{\delta x\to 0}{-sin(x+{\frac {\delta x}{2}})}=-sin(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/55a03f151abd8493abe60f7a34669d5d3e86577c height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {tg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6869fc8b8f66ef45dcb6974ef7616f04a034a910 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\cos ^{2}{x}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c02ca5cd6dd2e9891ae5cb6d895bf4026f57547a height: height attribute not set width: width attribute not set description: {\displaystyle \delta y=tg(x+\delta x)-tg(x)={\frac {sin(x+\delta x-x)}{cos(x+\delta x)\cdot cos(x)}}={\frac {sin(\delta x)}{cos(x+\delta x)\cdot cos(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5e92e5e3f75a1a307f047438b1c94c31e5ce790 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to 0}{\frac {\delta y}{\delta x}}=\lim _{\delta x\to 0}{\frac {\frac {sin(\delta x)}{cos(x+\delta x)\cdot cos(x)}}{\delta x}}=\lim _{\delta x\to 0}{\frac {sin(\delta x)}{\delta x}}\cdot } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc60bc78dddd2ab3d5cfcc35d43a468e33ab5263 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{\delta x\to 0}{\frac {1}{cos(x+\delta x)\cdot cos(x)}}={\frac {1}{cos^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f98fefbee423e53dd02101da9b26ca014c024c19 height: height attribute not set width: width attribute not set description: {\displaystyle (tgx)'=({\frac {sin(x)}{cos(x)}})'={\frac {(sin(x))'\cdot cos(x)-sin(x)\cdot (cos(x))'}{cos^{2}(x)}}={\frac {cos(x)\cdot cos(x)-sin(x)\cdot (-sin(x))}{cos^{2}(x)}}={\frac {cos^{2}(x)+sin^{2}(x)}{cos^{2}(x)}}={\frac {1}{cos^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/087bb7b7a8d45b2d4834f7169c3285f7639e976f height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {ctg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9082de6337a25e6f2a8d24f69d9cc37c7189e026 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{\sin ^{2}{x}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ed8c4951538f9cc803d0be28a79b4670d07d5980 height: height attribute not set width: width attribute not set description: {\displaystyle (ctgx)'=({\frac {cos(x)}{sin(x)}})'={\frac {(cos(x))'\cdot sin(x)-cos(x)\cdot (sin(x))'}{sin^{2}(x)}}={\frac {-sin(x)\cdot sin(x)+cos(x)\cdot cos(x)}{sin^{2}(x)}}=-{\frac {sin^{2}(x)+cos^{2}(x)}{sin^{2}(x)}}=-{\frac {1}{sin^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/897eb63b8464b4d198e9cccf9eaadb96e825f96d height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {sec} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/85fef187e5435f5c10d0d91c50b728f0f4a5e7c3 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {sec} \ x\cdot \mathrm {tg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/06a40fbec847d9d61a6b0d4708f6dc15b4240ed8 height: height attribute not set width: width attribute not set description: {\displaystyle (sec(x))'=({\frac {1}{cos(x)}})'={\frac {(1)'\cdot cos(x)-1\cdot (cos(x))'}{cos^{2}(x)}}={\frac {sin(x)}{cos^{2}(x)}}=sec(x)\cdot tg(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68dd71140dbe6c2a121c874ae101e40109b8c1ff height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cosec} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3ef14afc348d7c34561f7c1b559d2f0ea4d1f35 height: height attribute not set width: width attribute not set description: {\displaystyle -\mathrm {cosec} \ x\cdot \mathrm {ctg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91638aa1b69eb3b7a409d7beefe0880d428367a1 height: height attribute not set width: width attribute not set description: {\displaystyle (cosec(x))'=({\frac {1}{sin(x)}})'={\frac {(1)'\cdot sin(x)-1\cdot (sin(x))'}{sin^{2}(x)}}=-{\frac {cos(x)}{sin^{2}(x)}}=-coses(x)\cdot ctg(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24e4642c6150fe761607819d8f4b60484ca5deba height: height attribute not set width: width attribute not set description: {\displaystyle \arcsin {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cdd04fe3e7072b2351d97462e931fe2efe588f48 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7225463caa1c227cc3bcb308bb90a7fb48b9aba4 height: height attribute not set width: width attribute not set description: {\displaystyle sin(arcsin((x))=x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/be684108880964393fc7a90ba55f07de0e6d659a height: height attribute not set width: width attribute not set description: {\displaystyle [sin(arcsin((x))]'=x'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d87b0ada64658eeb5deec00575e25d4011c61f3 height: height attribute not set width: width attribute not set description: {\displaystyle cos(arcsin(x))\cdot (arcsin(x))'=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4e9028384761e793d1ee1c51665de88a0171ca86 height: height attribute not set width: width attribute not set description: {\displaystyle (arcsin(x))'={\frac {1}{cos(arcsin(x))}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/76b0ab93e0d8d6bb0ef2ef5392f5bed31547f346 height: height attribute not set width: width attribute not set description: {\displaystyle sin^{2}x+cos^{2}x=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b97428da3df92b7d7e3fe8bdd324d549420ff06d height: height attribute not set width: width attribute not set description: {\displaystyle (arcsin(x))'={\frac {1}{\pm {\sqrt {1-sin^{2}(arcsin(x))}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf2d89981edb4f950c9191723d160fe613831f5d height: height attribute not set width: width attribute not set description: {\displaystyle e(arcsin(x))=[-{\frac {\pi }{2}};{\frac {\pi }{2}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/34dcc41fa04bdaf9fe3ded8d564929e65000a6fc height: height attribute not set width: width attribute not set description: {\displaystyle (arcsin(x))'={\frac {1}{\sqrt {1-sin^{2}(arcsin(x))}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2450ffccfc68f04caaadb474572e0732e03ca220 height: height attribute not set width: width attribute not set description: {\displaystyle (arcsin(x))'={\frac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f46abe773aab02c04df96aa6f001ae98d11cb1c height: height attribute not set width: width attribute not set description: {\displaystyle \arccos {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b1f030cf90dca7c67045d6071d699297a75636 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/909a1c5d4004dd6bc0da4b075eaeb69d2a014428 height: height attribute not set width: width attribute not set description: {\displaystyle arcsin(x)+arccos(x)={\frac {\pi }{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3606594a168f2f06eb6faddfaac18f1c85324466 height: height attribute not set width: width attribute not set description: {\displaystyle [arcsin(x)+arccos(x)]'=({\frac {\pi }{2}})'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e8925c5820df1b790ab759063f08c09d5db407ba height: height attribute not set width: width attribute not set description: {\displaystyle (arcsin(x))'+(arccos(x))'=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45450396983ae2301fce6ab3b7f6ff6b06169eaa height: height attribute not set width: width attribute not set description: {\displaystyle (arccos(x))'=-(arcsin(x))'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b15081c0202fa469b53d2b4e3d46f6801935dcb9 height: height attribute not set width: width attribute not set description: {\displaystyle (arccos(x))'=-{\frac {1}{\sqrt {1-x^{2}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf1e6fedd84cd1837ca2ff00c12b886b5a53b700 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arctg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a59d1510d5b6f60a00f6c101d4bbba104e83bdc height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f9dd145b85cf50e49ed066070fdd9048d53211f0 height: height attribute not set width: width attribute not set description: {\displaystyle tg(arctg(x))=x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ce9406b214a5266d0bf8282fd6aae4b59602c66 height: height attribute not set width: width attribute not set description: {\displaystyle [tg(arctg(x))]'=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c280385e82dda45768b30ae4f618d76bc4dc2000 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{cos^{2}(arctg(x))}}\cdot (arctg(x))'=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/37bab589d82c1d38ee5f8880c49ee7c14d8016ad height: height attribute not set width: width attribute not set description: {\displaystyle (arctg(x))'=cos^{2}(arctg(x))} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c5378d066cf0168bf0210752a0113a44c3f8421 height: height attribute not set width: width attribute not set description: {\displaystyle cos(x)={\frac {1}{\sqrt {1+tg^{2}(x)}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e3cb4f6c9bf6ff31c580e69ea54834d16d13372 height: height attribute not set width: width attribute not set description: {\displaystyle (arctg(x))'=({\frac {1}{\sqrt {1+tg^{2}(arctg(x))}}})^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d742dda3b7e432ee571902752ea7ab1972b84385 height: height attribute not set width: width attribute not set description: {\displaystyle (arctg(x))'={\frac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2785231968d54f0c119eb43024967f7f18b63a height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arcctg} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bfda54d1b6ec07f0f779141175eb72ed24e5ea70 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f239a2e549f94b92072198ff9a53e65d137946f height: height attribute not set width: width attribute not set description: {\displaystyle arctg(x)+arcctg(x)={\frac {\pi }{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6f84cee67adf89ef76bfaa5c415907cce038d455 height: height attribute not set width: width attribute not set description: {\displaystyle [arctg(x)+arcctg(x)]'=({\frac {\pi }{2}})'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9cefc9862fd80599f47d6e20656486028b91553e height: height attribute not set width: width attribute not set description: {\displaystyle (arctg(x))'+(arcctg(x))'=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/630ebef6d9ac71773f07c14efdde1b1eabe645d5 height: height attribute not set width: width attribute not set description: {\displaystyle (arcctg(x))'=-(arctg(x))'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fce778f06c1192412ba385bb35c3478969ef2ddf height: height attribute not set width: width attribute not set description: {\displaystyle (arcctg(x))'=-{\frac {1}{1+x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/88ec2bd6f8abfaca4246dc08a6dedf9e9baec205 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arcsec} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de6666c725cda68d517a6284210b39c7d63945ae height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0028852722d49e428d984d23dc3f88c31b551d height: height attribute not set width: width attribute not set description: {\displaystyle arcsec(x)=arccos({\frac {1}{x}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/96724522efbbc47766263d582cb132fd9d783eb3 height: height attribute not set width: width attribute not set description: {\displaystyle (arcsec(x))'=(arccos({\frac {1}{x}}))'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eef82a84dae463c3402fff31e73f51dfd84a9cc8 height: height attribute not set width: width attribute not set description: {\displaystyle (arcsec(x))'=-{\frac {1}{\sqrt {1-{\frac {1}{x^{2}}}}}}\cdot (-{\frac {1}{x^{2}}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/85a257bdc812d5c0f3d0a9181860836bfb7db708 height: height attribute not set width: width attribute not set description: {\displaystyle (arcsec(x))'={\frac {1}{x^{2}{\sqrt {\frac {x^{2}-1}{x^{2}}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a7b52e2a79a7db366371e9ea5cb0e6dd5c2c9dff height: height attribute not set width: width attribute not set description: {\displaystyle (arcsec(x))'={\frac {1}{x^{2}{\frac {\sqrt {x^{2}-1}}{|x|}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/53193ae3488f6a6131cd552793acd35c379d196e height: height attribute not set width: width attribute not set description: {\displaystyle (arcsec(x))'={\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fcce723935e52560943a5138defeb011e328beae height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arccosec} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43ba0a9dfda26df21a71dc90a1871469606eeb76 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25087011b6822052b70b553bb25d2ebabc5dcfdc height: height attribute not set width: width attribute not set description: {\displaystyle arccosec(x)+arcsec(x)={\frac {\pi }{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4847d93af2226f3ab5e1ba20940ec8530526b49e height: height attribute not set width: width attribute not set description: {\displaystyle [arccosec(x)+arcsec(x)]'=({\frac {\pi }{2}})'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c82e8a1121fbfb5864d81226574bfb56651fdc2 height: height attribute not set width: width attribute not set description: {\displaystyle (arccosec(x))'+(arcsec(x))'=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab50918a522f382b03da37eb612689ecf482697 height: height attribute not set width: width attribute not set description: {\displaystyle (arccosec(x))'=-(arcsec(x))'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7bf22ef2a796af67713e86c52ea4b4a51d34aa9a height: height attribute not set width: width attribute not set description: {\displaystyle (arccosec(x))'=-{\frac {1}{|x|{\sqrt {x^{2}-1}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/511f2f93aa0d52ea2b20445e1eee67b38eb8513c height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {sh} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/825ef12399e41c1268140f1bb1a98f7e9420e781 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {ch} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2acfdcb4412c49e3b541c0fabcd2e643c1894e47 height: height attribute not set width: width attribute not set description: {\displaystyle (\operatorname {sh} {x})'=\left({\frac {e^{x}-e^{-x}}{2}}\right)'={\frac {1}{2}}\cdot (e^{x}-e^{-x})'={\frac {1}{2}}\cdot (e^{x}-(-1)\cdot e^{-x})={\frac {e^{x}+e^{-x}}{2}}=\operatorname {ch} {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6a5e591222de7de1d789d9ec6d0e73dfb2f737c6 height: height attribute not set width: width attribute not set description: {\displaystyle (\operatorname {ch} {x})'=\left({\frac {e^{x}+e^{-x}}{2}}\right)'={\frac {1}{2}}\cdot (e^{x}+e^{-x})'={\frac {1}{2}}\cdot (e^{x}+(-1)\cdot e^{-x})=\left({\frac {e^{x}-e^{-x}}{2}}\right)=\operatorname {sh} {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d4fea6511550020d084e61e026bb598d72a8f92f height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {th} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38f32843781cd772e8a5803e03611bc2fb364769 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\mathrm {ch} ^{2}\ x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b37f40894f44b1caa411915f54927ea1f8547f75 height: height attribute not set width: width attribute not set description: {\displaystyle (th(x))'=({\frac {sh(x)}{ch(x)}})'={\frac {(sh(x))'\cdot ch(x)-sh(x)\cdot (ch(x))'}{ch^{2}(x)}}={\frac {ch(x)\cdot ch(x)-sh(x)\cdot sh(x)}{ch^{2}(x)}}={\frac {ch^{2}(x)-sh^{2}(x)}{ch^{2}(x)}}={\frac {1}{ch^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f780c76dbccd6ba252466bab54a2321e793510a height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cth} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8d8bcd827fc57a1eae3086cddde1d0c1d326ef89 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{\mathrm {sh} ^{2}\ x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/16d010b4de57bdf3d0ccae3a1022406c83f81ee7 height: height attribute not set width: width attribute not set description: {\displaystyle (cthx)'=({\frac {ch(x)}{sh(x)}})'={\frac {(ch(x))'\cdot sh(x)-ch(x)\cdot (sh(x))'}{sh^{2}(x)}}={\frac {sh(x)\cdot sh(x)-ch(x)\cdot ch(x)}{sh^{2}(x)}}={\frac {sh^{2}(x)-ch^{2}(x)}{sh^{2}(x)}}=-{\frac {1}{sh^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/16e21b91a441c32a9011b661e75d16a2628e52bd height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {sch} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5b3fde859a9b532e36f184f5b976bf8ce3b5d510 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {\operatorname {sh} (x)}{\operatorname {ch} ^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/327af617d8e7429572fcbf9adb1029a8e20af8f5 height: height attribute not set width: width attribute not set description: {\displaystyle (sch(x))'=({\frac {1}{ch(x)}})'={\frac {(1)'\cdot ch(x)-1\cdot (ch(x))'}{ch^{2}(x)}}=-{\frac {sh(x)}{ch^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7787cddff7b4ec8667100cf95f4660e011eae9e6 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {csch} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9984307809201f3f86f980a58154f50bf0dbc57f height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {\operatorname {ch} (x)}{\operatorname {sh} ^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c058c8c5132df5df176417171e2fd61d2ecd3c24 height: height attribute not set width: width attribute not set description: {\displaystyle (csch(x))'=({\frac {1}{sh(x)}})'={\frac {(1)'\cdot sh(x)-1\cdot (sh(x))'}{sh^{2}(x)}}=-{\frac {ch(x)}{sh^{2}(x)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de02f2f6b35f140d2831feb6f9d6351d4134019f height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arsh} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84b3949748f5acaf6ef9c66da01bbde305bb1eef height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\sqrt {x^{2}+1}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44237ac7d962b06f9276211e07d95ab04f675b67 height: height attribute not set width: width attribute not set description: {\displaystyle (arsh(x))'=(\ln {(x+{\sqrt {x^{2}+1}})})'={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot (x+{\sqrt {x^{2}+1}})'={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot ((x)'+({\sqrt {x^{2}+1}})')={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot (1+({\sqrt {x^{2}+1}})')={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot (1+{\frac {1}{2{\sqrt {x^{2}+1}}}}\cdot (x^{2}+1)')={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot (1+{\frac {2x}{2{\sqrt {x^{2}+1}}}})={\frac {1}{x+{\sqrt {x^{2}+1}}}}\cdot ({\frac {x+{\sqrt {x^{2}+1}}}{\sqrt {x^{2}+1}}})={\frac {x+{\sqrt {x^{2}+1}}}{(x+{\sqrt {x^{2}+1}})\cdot ({\sqrt {x^{2}+1}})}}={\frac {1}{\sqrt {x^{2}+1}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/77664ae0993b526fb15156f24d9268c36c638e0f height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arch} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6691b6e9d91f0a16cc3c0368db3af6cdadbd1e8c height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\sqrt {x^{2}-1}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2adcca8a4e28603bfa0fec71899d8dda575a4826 height: height attribute not set width: width attribute not set description: {\displaystyle (arch(x))'=(\ln {(x+{\sqrt {x^{2}-1}})})'={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot (x+{\sqrt {x^{2}-1}})'={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot ((x)'+({\sqrt {x^{2}-1}})')={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot (1+({\sqrt {x^{2}-1}})')={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot (1+{\frac {1}{2{\sqrt {x^{2}-1}}}}\cdot (x^{2}-1)')={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot (1+{\frac {2x}{2{\sqrt {x^{2}-1}}}})={\frac {1}{x+{\sqrt {x^{2}-1}}}}\cdot ({\frac {x+{\sqrt {x^{2}-1}}}{\sqrt {x^{2}-1}}})={\frac {x+{\sqrt {x^{2}-1}}}{(x+{\sqrt {x^{2}-1}})\cdot ({\sqrt {x^{2}-1}})}}={\frac {1}{\sqrt {x^{2}-1}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a04a7c44c7b0ab41fba9699ecaeb2e42f9951d09 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arth} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a9b170261b6cae851c1771f9280ef69af8cc64ba height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{1-x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/21bbb9782850da0dc9e060e38ef39c4029e6ca3e height: height attribute not set width: width attribute not set description: {\displaystyle ({\displaystyle \mathrm {arth} \ x})'={\biggl (}{\frac {1}{2}}\cdot \ln {\biggl (}{\frac {1+x}{1-x}}{\biggl )}{\biggl )}'={\frac {1}{2}}\cdot {\frac {1-x}{1+x}}\cdot {\biggl (}{\frac {1+x}{1-x}}{\biggl )}'={\frac {1}{2}}\cdot {\frac {1-x}{1+x}}\cdot {\frac {(1+x)'(1-x)-(1+x)(1-x)'}{(1-x)^{2}}}={\frac {1}{2}}\cdot {\frac {1-x}{1+x}}\cdot {\frac {2}{(1-x)^{2}}}={\frac {1}{1-x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dd50917c69d4aab513487390dff189331ba4fed5 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arcth} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84e6bbb5100deb8a75a5f1e9f54f536d65976fa9 height: height attribute not set width: width attribute not set description: {\displaystyle ({\displaystyle \mathrm {arcth} \ x})'={\biggl (}{\frac {1}{2}}\cdot \ln {\biggl (}{\frac {x+1}{x-1}}{\biggl )}{\biggl )}'={\frac {1}{2}}\cdot {\frac {x-1}{x+1}}\cdot {\biggl (}{\frac {x+1}{x-1}}{\biggl )}'={\frac {1}{2}}\cdot {\frac {x-1}{x+1}}\cdot {\frac {(x+1)'(x-1)-(x+1)(x-1)'}{(x-1)^{2}}}={\frac {1}{2}}\cdot {\frac {x-1}{x+1}}\cdot {\frac {-2}{(x-1)^{2}}}={\frac {1}{1-x^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f79ec21891b891e0e769d384429e2ab1eba8b802 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arsech} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c13b8c6a307036df25a33537cd1af43514838dd1 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{x(x+1){\sqrt {\frac {1-x}{1+x}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d93009f71460588bbe51b9f596bceb8023ebb59e height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {arcsch} \ x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/41b37bd018191500fbf6b33685aa81c725963eb0 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{x(x+1){\sqrt {1+{\frac {1}{x^{2}}}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7216e69d28fdb11c29c859f015a284c1ec6f06ac height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {r} (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f60563b27243c915da8dc8585e1af1d7d206f17f height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}\mathbf {r} (t)=\lim _{h\to 0}{\frac {\mathbf {r} (t+h)-\mathbf {r} (t)}{h}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/93fef4e5ed0bb5822e04124d9563a1932a3613c8 height: height attribute not set width: width attribute not set description: {\displaystyle x'(t),\ y'(t),\ z'(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/884262fbc08349621f722cb454181eb2431bd8e4 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}(\mathbf {r_{1}} (t)+\mathbf {r_{2}} (t))={\frac {d\mathbf {r_{1}} (t)}{dt}}+{\frac {d\mathbf {r_{2}} (t)}{dt}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/758a36e5d56bf55d3d13dcfbf5a1b827c1273480 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}(f(t)\mathbf {r} (t))={\frac {df(t)}{dt}}\mathbf {r} (t)+f(t){\frac {d\mathbf {r} (t)}{dt}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6 height: height attribute not set width: width attribute not set description: {\displaystyle f(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3459b6c094448b518c387bc67e39c64dc5ca4d height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}(\mathbf {r_{1}} (t)\mathbf {r_{2}} (t))={\frac {d\mathbf {r_{1}} (t)}{dt}}\mathbf {r_{2}} (t)+\mathbf {r_{1}} (t){\frac {d\mathbf {r_{2}} (t)}{dt}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b172aa52700f4bc10de3dc186111a82e2465a50 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}[\mathbf {r_{1}} (t),\mathbf {r_{2}} (t)]=\left[{\frac {d\mathbf {r_{1}} (t)}{dt}},\mathbf {r_{2}} (t)\right]+\left[\mathbf {r_{1}} (t),{\frac {d\mathbf {r_{2}} (t)}{dt}}\right]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f9d7246ea3b38c4846eaa6d46134c47d6c49bb7 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {d}{dt}}(\mathbf {a} (t),\mathbf {b} (t),\mathbf {c} (t))=\left({\frac {d\mathbf {a} (t)}{dt}},\mathbf {b} (t),\mathbf {c} (t)\right)+\left(\mathbf {a} (t),{\frac {d\mathbf {b} (t)}{dt}},\mathbf {c} (t)\right)+\left(\mathbf {a} (t),\mathbf {b} (t),{\frac {d\mathbf {c} (t)}{dt}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/721a6a7321968703beb98b235f95ac23a8cda9ad height: height attribute not set width: width attribute not set description: {\displaystyle d_{x}^{q}f(x)={\frac {f(qx)-f(x)}{(q-1)x}}.} |
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