{"id":385,"date":"2023-07-03T16:55:30","date_gmt":"2023-07-03T16:55:30","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\/"},"modified":"2023-07-03T16:55:30","modified_gmt":"2023-07-03T16:55:30","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","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\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0430\u0440\u043a\u0441\u0438\u043d\u0443\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\u044b\u0445 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0434\u0430\u0436\u0435 \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, \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\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-arcoseno\"><\/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\u0441\u0438\u043d\u0443\u0441\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0410\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u043d\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f x \u0440\u0430\u0432\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043a\u043e\u0440\u043d\u044f \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-924f0591661727fa46ea5f69bff39401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" 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\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u0440\u0430\u0432\u043d\u0430 \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 \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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e \u0432\u0442\u043e\u0440\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435. <\/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-de-larcosine.webp\" alt=\"\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430\" class=\"wp-image-1952\" width=\"403\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441 \u2014 \u044d\u0442\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u0435\u0449\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u043c \u0441\u0438\u043d\u0443\u0441\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcoseno\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0432\u0438\u0434\u0435\u0432, \u043a\u0430\u043a\u043e\u0432\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\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. \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\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-arcoseno-de-2x\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\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-61368fb29b840d3583de92c8e6202006_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0439 \u0435\u0439 \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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\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\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 2, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u043e\u0434\u043d\u043e\u0433\u043e \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-b0282aa3f00df6b3bd1046fff94fa586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"550\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcoseno-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\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-a4962743c0667c1443d315dd330bf3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u043b\u044f \u0435\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f x <sup>2<\/sup> \u0438\u043c\u0435\u0435\u0442 \u0432\u0442\u043e\u0440\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 2x. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430 x, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c 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-60a677a7b7ca12bf048e6d20aca7b122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"538\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcoseno-de-ex\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430 e <sup>x<\/sup><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-0843fbec2d0e53f9f16fd8e704af9763_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f e <sup>x<\/sup> \u0440\u0430\u0432\u043d\u0430 \u0441\u0430\u043c\u043e\u0439 \u0441\u0435\u0431\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\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-e836cc1a00000f86d4f8891a12f4997d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{e^x}{\\sqrt{1-\\left(e^x\\right)^2}}=\\cfrac{e^x}{\\sqrt{1-e^{2x}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"542\" 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-arcoseno\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430<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 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u043d\u044b\u0435 \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-515f2956c43c783ea330e8b3addf908c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arcsen}(6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" 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-537773e0ce262d3f14bb6af61b6d5d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arcsen}(x^2-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-d2ed0ca6a00694c6b35b651d9e206bbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arcsen}\\left(3x^4-6x^3+9+e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"304\" 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-c3b5ab58c98e35c39ea82368aebabded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arcsen}\\left(\\log_5(3x)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"212\" 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-25cafb754c9abd936852c9884fa1d9ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arcsen}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"182\" 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-3d8fcc06d1afecc77f744ddddafc702f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=\\cfrac{6}{\\sqrt{1-(6x)^2}}=\\cfrac{6}{\\sqrt{1-36x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"287\" 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-4491410567de31ccb0be97922264ca90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{2x-4}{\\sqrt{1-(x^2-4x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"219\" 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-b436dbd761b2261168c506e7e2e0d246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f'(x)=\\cfrac{12x^3-18x^2+2x\\cdot e^{x^2}}{\\sqrt{1-(3x^4-6x^3+9+e^{x^2})^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"311\" style=\"vertical-align: -21px;\"><\/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-57f2d6846bdde50321c1387f949d983a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{1}{\\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 5}=\\cfrac{1}{x\\cdot \\ln 5\\cdot \\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"519\" style=\"vertical-align: -30px;\"><\/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-0a82c0fd18a8672100ed3b79525a1028_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=\"253\" 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-arcoseno\"><\/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\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u0430\u043b\u0435\u0435 \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u043c \u043a \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\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-139a7a695d83cf004f32f983b10bde10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arcsen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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\u0441\u0438\u043d\u0443\u0441 \u0432 \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-443f95e83265d63f8d88d8782d014011_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{sen}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u043e\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\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-1a653163fb7285dbfafcbaaa4b80031e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\text{cos}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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-ac9839cbaf86cd3bcd2020ae70eb57e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{cos}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"86\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0414\u0430\u043b\u0435\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\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:<\/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-d5c5551414baf4b4a0f28a4eac057ae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{cos}(y)=\\sqrt{1-\\text{sen}^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-0535c541ff9c3a80c457aae33b359bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{1-\\text{sen}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> \u0418, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u044b\u0448\u0435 \u043c\u044b \u043f\u0440\u0438\u0448\u043b\u0438 \u043a \u0432\u044b\u0432\u043e\u0434\u0443, \u0447\u0442\u043e x \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u0441\u0438\u043d\u0443\u0441\u0443 y, \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \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-6fafe005791d06de3e64e76eda0ac194_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=\"103\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u044d\u0442\u0443 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0443, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \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\u0441\u0438\u043d\u0443\u0441\u0430, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u0447\u0442\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0430\u0440\u043a\u0441\u0438\u043d\u0443\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\u044b\u0445 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0434\u0430\u0436\u0435 \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, \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\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\u0441\u0438\u043d\u0443\u0441\u0430? \u0410\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u043d\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f x \u0440\u0430\u0432\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043a\u043e\u0440\u043d\u044f \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\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\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\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u0430<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 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