{"id":803,"date":"2014-01-04T02:50:06","date_gmt":"2014-01-03T18:50:06","guid":{"rendered":"http:\/\/soniuch.net\/?page_id=803"},"modified":"2014-01-04T02:50:06","modified_gmt":"2014-01-03T18:50:06","slug":"%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb-%d1%82%d0%be%d0%be%d0%bb%d0%be%d0%bb-%d1%83%d0%bb%d0%b0%d0%bc%d0%b6%d0%bb%d0%b0%d0%bb","status":"publish","type":"page","link":"https:\/\/soniuch.net\/?page_id=803","title":{"rendered":"\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b \u0442\u043e\u043e\u043b\u043e\u043b (\u0423\u043b\u0430\u043c\u0436\u043b\u0430\u043b)"},"content":{"rendered":"

\u041d\u044d\u0433\u0434\u04af\u0433\u044d\u044d\u0440<\/strong> \u0433\u0430\u0439\u0445\u0430\u043c\u0448\u0438\u0433\u0442 \u0445\u044f\u0437\u0433\u0430\u0430\u0440:<\/strong><\/span><\/p>\n

$$\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1$$<\/p>\n

\u0425\u043e\u0451\u0440\u0434\u0443\u0433\u0430\u0430\u0440 \u0433\u0430\u0439\u0445\u0430\u043c\u0448\u0438\u0433\u0442 \u0445\u044f\u0437\u0433\u0430\u0430\u0440:<\/strong><\/span><\/p>\n

$$\\lim_{x \\to \\infty} \\big( 1 + \\frac{1}{x} \\big)^x = e$$<\/p>\n

\u0423\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/strong><\/span><\/p>\n

$x_\\circ$ \u0446\u044d\u0433 \u0434\u044d\u044d\u0440\u0445 $y=f(x)$ \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b \u0433\u044d\u0434\u044d\u0433 \u043d\u044c:<\/p>\n

$$f'(x_\\circ) = \\lim_{\\Delta x \\to 0} \\frac{f(x_0 + \\Delta x) – f(x_0)}{\\Delta x}$$<\/p>\n

\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b<\/strong><\/span><\/p>\n

$y=f(x)$ \u0444\u0443\u043d\u043a\u0446\u044b\u043d $x_\\circ$ \u0446\u044d\u0433 \u0434\u0430\u0445\u044c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b \u043d\u044c $$dy = f'(x_\\circ)dx$$<\/p>\n

\u042d\u0433\u044d\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b\u0443\u0443\u0434<\/strong><\/span><\/p>\n

\u041d\u0438\u0439\u043b\u0431\u044d\u0440\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span> $$(u+v)’ = u’ + v’$$<\/p>\n

\u04ae\u0440\u0436\u0432\u044d\u0440\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span> $$(u v)’ = u’ v + v’ u$$ $$C$$ \u0442\u043e\u0433\u0442\u043c\u043e\u043b \u0431\u043e\u043b $$!(Cu)’=Cu’ $$<\/p>\n

\u041d\u043e\u0433\u0434\u0432\u043e\u0440\u044b\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span> $$\\big( \\frac{u}{v}\\big)’ = \\frac{u’v – u v’}{v^2}$$<\/p>\n

\u0417\u044d\u0440\u044d\u0433\u0442 \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span> $$\\big( x^n\\big)’ = n x^{n-1}$$<\/p>\n

$$(\\sqrt{x})’=\\frac{1}{2\\sqrt{x}}$$<\/p>\n

$$\\big(\\frac{1}{x}\\big)’=(x^{-1})’=-\\frac{1}{x^2}$$<\/p>\n

\u0418\u043b\u0442\u0433\u044d\u0433\u0447 \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span> $$\\big( a^x\\big)’=a^x \\ln a$$<\/p>\n

$$\\big( e^x\\big)’ = e^x$$<\/p>\n

\u041b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span><\/p>\n

$$(\\log_a x)’=\\frac{1}{x \\ln a}$$<\/p>\n

$$(\\ln x)’ = \\frac{1}{x}$$<\/p>\n

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span><\/p>\n

$$(\\sin x)’ = \\cos x$$<\/p>\n

$$(\\cos x)’ = – \\sin x$$<\/p>\n

$$(\\textrm{tg} x = \\frac{1}{\\cos x} = \\sec^2 x)’$$<\/p>\n

$$(\\textrm{ctg} x)’ = – \\frac{1}{\\sin^2 x} = – \\textrm{cosec}^2 x$$<\/p>\n

$$(\\arcsin x)’= \\frac{1}{\\sqrt{1-x^2}}$$<\/p>\n

$$(\\arccos x)’= – \\frac{1}{\\sqrt{1-x^2}}$$<\/p>\n

$$(\\textrm{arctg} x)’= \\frac{1}{1+x^2}$$<\/p>\n

$$(\\textrm{arcctg} x)’= – \\frac{1}{1+x^2}$$<\/p>\n

\u0414\u0430\u0432\u0445\u0430\u0440 \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span>
\n$y=f(x) = f(\\varphi(t))$ \u0433\u044d\u0441\u044d\u043d \u0434\u0430\u0432\u0445\u0430\u0440 \u0444\u0443\u043d\u043a\u0446 \u04e9\u0433\u04e9\u0433\u0434\u0441\u04e9\u043d \u0431\u0430\u0439\u0433. $t_\\circ$ \u0446\u044d\u0433 \u0434\u044d\u044d\u0440 $x_\\circ = \\varphi(t_\\circ)$ \u0433\u044d\u0441\u044d\u043d \u04af\u0433. \u042d\u043d\u044d \u0434\u0430\u0432\u0445\u0430\u0440 \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d\u00a0 \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b \u043d\u044c $t_\\circ$ \u0446\u044d\u0433 \u0434\u044d\u044d\u0440<\/p>\n

$$y'(t_\\circ) = f'(x_\\circ) \\cdot \\varphi'(t_\\circ)$$<\/p>\n

\u0423\u0440\u0432\u0443\u0443 \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b:<\/span><\/p>\n

$y=f(x)$ \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0443\u0440\u0432\u0443\u0443 \u0444\u0443\u043d\u043a\u0446 \u043d\u044c $x=\\varphi(y)$ \u0431\u0430\u0439\u0433. $x_\\circ$ \u0446\u044d\u0433 \u0434\u044d\u044d\u0440 $y_\\circ = f(x_\\circ)$ \u0431\u0430\u0439\u043d\u0430. \u042d\u043d\u044d \u0445\u043e\u0451\u0440 \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b \u043d\u044c \u0443\u0433 \u0446\u044d\u0433 \u0434\u044d\u044d\u0440<\/p>\n

$$\\varphi'(y_\\circ) = \\frac{1}{f'(x_\\circ)}$$<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u041d\u044d\u0433\u0434\u04af\u0433\u044d\u044d\u0440 \u0433\u0430\u0439\u0445\u0430\u043c\u0448\u0438\u0433\u0442 \u0445\u044f\u0437\u0433\u0430\u0430\u0440: $$\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1$$ \u0425\u043e\u0451\u0440\u0434\u0443\u0433\u0430\u0430\u0440 \u0433\u0430\u0439\u0445\u0430\u043c\u0448\u0438\u0433\u0442 \u0445\u044f\u0437\u0433\u0430\u0430\u0440: $$\\lim_{x \\to \\infty} \\big( 1 + \\frac{1}{x} \\big)^x = e$$ \u0423\u043b\u0430\u043c\u0436\u043b\u0430\u043b: $x_\\circ$ \u0446\u044d\u0433 \u0434\u044d\u044d\u0440\u0445 $y=f(x)$ \u0444\u0443\u043d\u043a\u0446\u0438\u0439\u043d \u0443\u043b\u0430\u043c\u0436\u043b\u0430\u043b \u0433\u044d\u0434\u044d\u0433 \u043d\u044c: $$f'(x_\\circ) = \\lim_{\\Delta x \\to 0} \\frac{f(x_0 + \\Delta x) – f(x_0)}{\\Delta x}$$ \u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b $y=f(x)$ \u0444\u0443\u043d\u043a\u0446\u044b\u043d $x_\\circ$ \u0446\u044d\u0433 \u0434\u0430\u0445\u044c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b \u043d\u044c $$dy =… Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":713,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-803","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=803"}],"version-history":[{"count":0,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/803\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/713"}],"wp:attachment":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}