{"id":391,"date":"2023-07-03T10:10:06","date_gmt":"2023-07-03T10:10:06","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d0%b0%d1%80%d0%ba%d0%ba%d0%be%d0%b7%d0%b8\/"},"modified":"2023-07-03T10:10:06","modified_gmt":"2023-07-03T10:10:06","slug":"%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d0%b0%d1%80%d0%ba%d0%ba%d0%be%d0%b7%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d0%b0%d1%80%d0%ba%d0%ba%d0%be%d0%b7%d0%b8\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0432\u0438\u0434\u0438\u0442\u0435, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430). \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\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 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u0430\u0441 \u0436\u0434\u0435\u0442 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \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. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-arcocoseno-hiperbolico\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043f\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c\u0443 \u043a\u043e\u0440\u043d\u044e \u0438\u0437 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u043c\u0438\u043d\u0443\u0441 1.<\/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-cf6cb0ef7aae071322695ae7c8455d1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{\\sqrt{x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"426\" 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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043e\u043a\u043e\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 \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0439 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043c\u0438\u043d\u0443\u0441 \u043e\u0434\u0438\u043d.<\/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-675bee296952a25c6048af071e7ce4e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"427\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0412\u0442\u043e\u0440\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0432 \u0441\u0435\u0431\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0438 \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u043e\u0436\u0435\u0442 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u043b\u044e\u0431\u043e\u0433\u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438, \u0435\u0441\u043b\u0438 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c x \u043d\u0430 u, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043f\u0435\u0440\u0432\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443. \u0412\u043c\u0435\u0441\u0442\u043e \u044d\u0442\u043e\u0433\u043e \u043f\u0435\u0440\u0432\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 x. <\/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\/derivee-de-larccosine-hyperbolique.webp\" alt=\"\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\" class=\"wp-image-2337\" width=\"403\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u0442\u0438 \u0434\u0432\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0432\u044f\u0437\u0430\u043d\u044b. \u0412\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \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, \u043d\u0430\u0436\u0430\u0432 \u0437\u0434\u0435\u0441\u044c:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 <\/span> <span style=\"text-decoration: underline;\"><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcoseno-hiperbolico\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \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<h3 class=\"wp-block-heading\" id=\"block-46cfc7df-b680-41c2-ad53-bd8a19834b32\"> \u041f\u0440\u0438\u043c\u0435\u0440 1<\/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-83158beb1fa0dda8f8a6469cc6f87cd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-2a112ce1-0dbe-43d5-95b3-4d8506c1a246\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\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-675bee296952a25c6048af071e7ce4e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"427\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-a4fe1876-f662-49c1-8d09-6a6c4b5528dd\"> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043e\u0442 5\u0445, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0440\u0430\u0432\u043d\u0430 5. \u0410 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u044c \u043a\u043e\u0440\u0435\u043d\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0438\u0437 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0439 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043c\u0438\u043d\u0443\u0441 1: <\/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-8704c0fb8ce82efc60e67bbca363b205_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(5x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{5}{\\sqrt{(5x)^2-1}}=\\cfrac{5}{\\sqrt{25x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"567\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" id=\"block-1446420a-0d61-44d3-9e31-8c5935a432a7\"> \u041f\u0440\u0438\u043c\u0435\u0440 2<\/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-07f0e806641b4f8ddc3441faa6059bc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(x^4-5x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-0514a2ea-d85a-4b25-a7db-9c27533e7436\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0438\u0437 \u044d\u0442\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0435\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\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-675bee296952a25c6048af071e7ce4e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"427\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-6abf3c5a-c400-48c6-8375-c05fcb255b20\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435 \u0437\u0430\u043f\u0438\u0448\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0430 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 &#8212; \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0433\u043e \u0432 2 \u043c\u0438\u043d\u0443\u0441 1: <\/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-376cce9ffe78b04c056d4aa90af1be3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosh}(x^4-5x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{4x^3-10x}{\\sqrt{\\left(x^4-5x^2\\right)^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"555\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-del-arcocoseno-hiperbolico\"><\/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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\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-48f91a3e46d7a7275e54619efd3ede1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" 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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0432 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \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-7032f56de52ca8602783ca5f4bbb0767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cosh}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412\u044b\u0432\u043e\u0434\u0438\u043c \u0438\u0437 \u043e\u0431\u0435\u0438\u0445 \u0447\u0430\u0441\u0442\u0435\u0439 \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-56122b4a5ee02b2c4c6f62751b5b21b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\text{senh}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" 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-7848ebafab6456313be4d737917b898a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{senh}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"97\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \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, \u0441\u0432\u044f\u0437\u044b\u0432\u0430\u044e\u0449\u0435\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c:<\/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-c45c9cefda55a71bba2eb8cfe1c3a861_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(y)-\\text{senh}^2(y)=1 \\ \\longrightarrow \\ \\text{senh}(y)=\\sqrt{\\text{cosh}^2(y)-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"428\" style=\"vertical-align: -9px;\"><\/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-5b7a01a3b50f15a8b5ac0df596cfb1e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{\\text{cosh}^2(y)-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"152\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \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-01f9e07a0c0f68a771edda2395685299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"103\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"articulos-relacionados\"><\/span> \u041f\u043e\u0445\u043e\u0436\u0438\u0435 \u0442\u043e\u0432\u0430\u0440\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> <span style=\"text-decoration: underline;\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441\u0430 <\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0430\u0440\u043a\u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441\u0430 <\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441\u0430 <\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0437\u0438\u043d\u0430 <\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 <\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0432\u0438\u0434\u0438\u0442\u0435, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430). \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\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 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u0430\u0441 \u0436\u0434\u0435\u0442 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \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. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u0440\u043a\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0435 \u043f\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c\u0443 \u043a\u043e\u0440\u043d\u044e \u0438\u0437 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u043c\u0438\u043d\u0443\u0441 1. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d0%b0%d1%80%d0%ba%d0%ba%d0%be%d0%b7%d0%b8\/\"> <span 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