{"id":386,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","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%be%d0%b5-%d0%bb%d0%b0%d1%80%d0%ba%d0%be%d0%b7%d0%b8%d0%bd%d0%b0-2\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d0%bb%d0%b0%d1%80%d0%ba%d0%be%d0%b7%d0%b8%d0%bd%d0%b0-2","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%be%d0%b5-%d0%bb%d0%b0%d1%80%d0%ba%d0%be%d0%b7%d0%b8%d0%bd%d0%b0-2\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044f \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, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span> \u0427\u0442\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\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 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c\u0443 \u043a\u043e\u0440\u043d\u044e \u0438\u0437 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043c\u0438\u043d\u0443\u0441 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435.<\/strong><\/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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, <strong>\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u0440\u0430\u0432\u043d\u0430 \u043c\u0438\u043d\u0443\u0441 \u0447\u0430\u0441\u0442\u043d\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043c\u0438\u043d\u0443\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u044d\u0442\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438, \u043f\u0435\u0440\u0432\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043f\u0443\u0442\u0435\u043c \u0437\u0430\u043c\u0435\u043d\u044b x \u043d\u0430 u \u0432\u043e \u0432\u0442\u043e\u0440\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435. \u0418\u0442\u0430\u043a, \u043f\u043e\u0434\u0432\u0435\u0434\u0435\u043c \u0438\u0442\u043e\u0433: \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derive-arc-cosinus.webp\" alt=\"\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u0430 <span style=\"text-decoration: underline;\"> \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430 <\/span> , \u043d\u043e \u0441 \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u043f\u0435\u0440\u0435\u0434 \u043d\u0435\u0439 \u043c\u0438\u043d\u0443\u0441\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u043c\u044b \u0441\u0435\u0439\u0447\u0430\u0441 \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0442\u0430\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \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. \u0422\u0430\u043a \u0432\u0430\u043c \u0431\u0443\u0434\u0435\u0442 \u043b\u0435\u0433\u0447\u0435 \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcocoseno-de-2x\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u043e\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f 2x \u0440\u0430\u0432\u043d\u0430 2, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043d\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f 2x \u0440\u0430\u0432\u043d\u0430 \u043c\u0438\u043d\u0443\u0441 2 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043a\u043e\u0440\u043d\u0435\u0432\u043e\u0439 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043c\u0438\u043d\u0443\u0441 2x \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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\sqrt{1-(2x)^2}}=-\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"576\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 2: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0441 \u043f\u0440\u0430\u0432\u0438\u043b\u043e\u043c \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 x <sup>2<\/sup> \u0440\u0430\u0432\u043d\u0430 2x, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 x \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 2 \u0440\u0430\u0432\u043d\u0430: <\/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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=-\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"565\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcocoseno-de-un-logaritmo\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0443\u044e \u0438\u0437 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0435\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \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.<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u0440\u0430\u0432\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0435, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 x, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0446\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430: <\/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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcocoseno\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0440\u0435\u0448\u0438\u043b\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: <\/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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" 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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" 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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" 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>\u043f\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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" 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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" 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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" style=\"vertical-align: 0px;\"><\/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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" style=\"vertical-align: 0px;\"><\/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-d1a362c38a56084dec3c6ebbccba9ab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =-\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=-\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=-\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"267\" style=\"vertical-align: 0px;\"><\/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-formula-de-la-derivada-del-arcocoseno\"><\/span> \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u044d\u0442\u043e\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 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430.<\/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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0432 \u043a\u043e\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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0434\u0432\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430:<\/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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u043e\u0447\u0438\u0449\u0430\u0435\u043c \u0432\u0430\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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e, \u0447\u0442\u043e\u0431\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u0438\u043d\u0443\u0441 \u043d\u0430 \u043a\u043e\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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" style=\"vertical-align: -6px;\"><\/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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> \u041d\u043e \u0432\u044b\u0448\u0435 \u043c\u044b \u043f\u0440\u0438\u0448\u043b\u0438 \u043a \u0432\u044b\u0432\u043e\u0434\u0443, \u0447\u0442\u043e x \u0440\u0430\u0432\u0435\u043d \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0443 y, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f:<\/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-8c3b21ba43e58ec763ab27498aa4fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0418 \u0432\u043e\u0442 \u043c\u044b \u043f\u0440\u0438\u0448\u043b\u0438 \u043a \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430, \u0432\u043e\u0442 \u0438 \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0430 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044f \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, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. \u0427\u0442\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430? \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\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 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c\u0443 \u043a\u043e\u0440\u043d\u044e \u0438\u0437 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043c\u0438\u043d\u0443\u0441 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 &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%be%d0%b5-%d0%bb%d0%b0%d1%80%d0%ba%d0%be%d0%b7%d0%b8%d0%bd%d0%b0-2\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\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-386","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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