{"id":50,"date":"2023-09-17T10:54:18","date_gmt":"2023-09-17T10:54:18","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d1%82%d0%b0%d0%bd%d0%b3%d0%b5%d0%bd%d1%81%d0%b0\/"},"modified":"2023-09-17T10:54:18","modified_gmt":"2023-09-17T10:54:18","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d1%82%d0%b0%d0%bd%d0%b3%d0%b5%d0%bd%d1%81%d0%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d1%82%d0%b0%d0%bd%d0%b3%d0%b5%d0%bd%d1%81%d0%b0\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0438 \u0434\u0430\u0436\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0434\u043e\u043a\u0430\u0436\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043f\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u0441\u0438\u043d\u0443\u0441\u0430 x.<\/strong> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0432\u043d\u0430 \u043c\u0438\u043d\u0443\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441\u0430 x \u0438 \u043c\u0438\u043d\u0443\u0441 \u0441\u0443\u043c\u043c\u0435 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043f\u043b\u044e\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a3653f5c765d773ebc789107bf1a825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{1}{\\text{sen}^2(x)}=-\\text{cosec}^2(x)=-\\left(1+\\text{cotg}^2(x)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"393\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0415\u0441\u043b\u0438 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0439 \u043e\u0442 x, \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0442\u0430\u043a\u0438\u0435 \u0436\u0435, \u043a\u0430\u043a \u0438 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0435, \u043d\u043e \u0441 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430.<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-38ea1d1edeaf5664c56a946b5a87577d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}=-u' \\cdot \\text{cosec}^2(u)=-u' \\cdot \\left(1+\\text{cotg}^2(u)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0442\u0440\u0438 \u0440\u0430\u0437\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. \u041d\u043e, \u043f\u043e \u043b\u043e\u0433\u0438\u043a\u0435 \u0432\u0435\u0449\u0435\u0439, \u043d\u0435\u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0441\u0435 \u0442\u0440\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u0430 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u043f\u043e \u0442\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432\u0430\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0440\u0430\u0432\u0438\u0442\u0441\u044f. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-de-la-cotangente.webp\" alt=\"\u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0438\u0437 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430\" class=\"wp-image-2685\" width=\"428\" height=\"361\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cotangente\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0432 \u044d\u0442\u043e\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u0440\u0435\u0448\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cotangente-de-2x\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 2x.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b95db136ea1e222c9f810d724216b083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438, \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043e\u0434\u043d\u0443 \u0438\u0437 \u0442\u0440\u0435\u0445 \u0444\u043e\u0440\u043c\u0443\u043b, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u0445 \u0432\u044b\u0448\u0435. \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 2x \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u043b\u0435\u043d\u043e\u043c \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0435\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 2. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 2x \u0440\u0430\u0432\u043d\u0430 \u043c\u0438\u043d\u0443\u0441 \u0434\u0432\u0443\u043c, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u043c \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0441\u0438\u043d\u0443\u0441\u0430 2x: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4151decbf7dd792fd0ea6aa6ca4b55f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"426\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cotangente-de-x-al-cuadrado\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 2: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0412\u043e \u0432\u0442\u043e\u0440\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ec3733080f720a5115d2d6719d33d7e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f x, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438, \u0447\u0442\u043e\u0431\u044b \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441.<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u0440\u0430\u0432\u043d\u0430 2x, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x <sup>2<\/sup> \u0440\u0430\u0432\u043d\u0430: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6aef87160d0da1da0b32e1e200f31b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cotangente-al-cubo\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0432 \u043a\u0443\u0431\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043d\u0430\u0439\u0434\u0435\u043c, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u0443\u0431\u0430 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9be8c3c10c50e3ef6bb701a11d3f46c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}^3(x^5-6x^2+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed0c6f314584b0f00021e3833de2b223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=-3\\cdot\\text{cotg}^2(x^5-6x^2+10)\\cdot\\frac{5x^4-12x}{\\text{sen}^2(x^5-6x^2+10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-cotangente\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u043e\u0432: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e1e391853b53d81ed500fd590799cbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{cotg}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8581122adcd9d79db9862a27b57af0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{cotg}(2x^4+10x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7814ccc95124c55f86b2f7036178254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=\\text{cotg}^5\\left(\\frac{x}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"160\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dcf8b02c8e9d9712210a78d116e2fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cotg}\\left(e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f358f9329696ee71ac2c1abfd5f9668e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{cotg}\\bigl(\\ln(x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"176\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e26ae47cb88a301a3353d868fc9b74f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{cotg}\\left(\\sqrt{8x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"166\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b002740b34952198a8284265a444cbed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=-\\cfrac{5}{\\text{sen}^2(5x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"171\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9b86f549fab91f93d0fc4e437e1c4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=-\\cfrac{8x+10}{\\text{sen}^2(2x^4+10x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb1435fb7eb0c7bcff84741362417548_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)\\cdot \\left(-\\frac{1}{\\text{sen}^2\\left(\\frac{x}{2}\\right)}\\right)\\cdot \\frac{1}{2}=-\\frac{5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)}{2\\cdot \\text{sen}^2\\left(\\frac{x}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"468\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fb5fc0cea94ec46660b5bb16d9daaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-\\cfrac{2x\\cdot e^{x^2}}{\\text{sen}^2(e^{x^2})}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"175\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-efc6c63eb1a5cfc3f89deb4cfc3b4586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=-\\cfrac{\\cfrac{2x}{x^2}}{\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}=-\\cfrac{2}{x\\cdot\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"356\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-70d6c7ac291ee53490646ae841842eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-\\cfrac{\\frac{8}{2\\sqrt{8x}}}{\\text{sen}^2\\left(\\sqrt{8x}\\right)}=-\\cfrac{4}{\\sqrt{8x}\\cdot \\text{sen}^2\\left(\\sqrt{8x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"360\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-la-cotangente\"><\/span> \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u0447\u043d\u0435\u043c \u0441 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0440\u0430\u0432\u0435\u043d \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0443, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u0441\u0438\u043d\u0443\u0441:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd85e2f7ac86aa67c6bd2f82fedfa926_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}(x)=\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"131\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u043d\u043e\u0433\u043e; <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0eb90358967efc64de6d45b8eabe5e37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{cotg}(x)\\bigr)'=\\left(\\frac{\\text{cos}(x)}{\\text{sen}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"181\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7685acfe693a3c5e8dd2e543ad8ec7c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}(x)\\cdot \\text{sen}(x)-\\text{cos}(x)\\cdot \\text{cos}(x) }{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"349\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9988024649ed4fdb4b1a9bb913aa813f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}^2(x)-\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"243\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0411\u0435\u0440\u0435\u043c \u043e\u0431\u0449\u0438\u0439 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u044c \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0438 \u0443\u0431\u0438\u0440\u0430\u0435\u043c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0437\u043d\u0430\u043a \u0438\u0437 \u0434\u0440\u043e\u0431\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b23352ad101cdc7e1adeb6316c6d66c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\bigl(\\text{sen}^2(x)+\\text{cos}^2(x)\\bigr)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"259\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0441\u0438\u043d\u0443\u0441\u0430 \u043f\u043b\u044e\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0440\u0430\u0432\u0435\u043d \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u0431\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0443.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92d80771f891319379b2e756c5524aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(x)+\\text{cos}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd14ec817754afcafd5d862afc0703b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{1}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"157\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0418 \u043c\u044b \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043f\u0435\u0440\u0432\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e\u0439 \u0438\u043d\u0432\u0435\u0440\u0441\u0438\u0435\u0439 \u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0442\u043e\u0440\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0442\u0430\u043a\u0436\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41aafad77ef896612fe6851ee97d914a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\text{sec}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0442\u0440\u0435\u0442\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u044d\u0442\u043e\u0439 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043e\u0436\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0432 \u0434\u0440\u043e\u0431\u044c \u0438\u0437 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0448\u0430\u0433\u0430 \u0432 \u0441\u0443\u043c\u043c\u0443 \u0434\u0440\u043e\u0431\u0435\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3780e44f1c85235473d47f418c7bc889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cotg}'(x)=-\\left(\\frac{\\text{sen}^2(x)}{\\text{sen}^2(x)}+\\frac{\\text{cos}^2(x)}{\\text{sen}^2(x)}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"266\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7a8b05807749ddd4b8979253dcb2f45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=-\\bigl(1+\\text{cotg}^2(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"200\" style=\"vertical-align: -7px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u0438 \u0434\u0430\u0436\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0434\u043e\u043a\u0430\u0436\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043f\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u0441\u0438\u043d\u0443\u0441\u0430 x. \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 x \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0432\u043d\u0430 \u043c\u0438\u043d\u0443\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0443 \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441\u0430 x \u0438 \u043c\u0438\u043d\u0443\u0441 \u0441\u0443\u043c\u043c\u0435 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043f\u043b\u044e\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d1%82%d0%b0%d0%bd%d0%b3%d0%b5%d0%bd%d1%81%d0%b0\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-50","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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