{"id":395,"date":"2023-07-03T02:54:42","date_gmt":"2023-07-03T02:54:42","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivada-da-cossecante-hiperbolica\/"},"modified":"2023-07-03T02:54:42","modified_gmt":"2023-07-03T02:54:42","slug":"derivada-da-cossecante-hiperbolica","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivada-da-cossecante-hiperbolica\/","title":{"rendered":"Derivada da cossecante hiperb\u00f3lica"},"content":{"rendered":"<p>Neste artigo explicamos como derivar a cossecante hiperb\u00f3lica de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea poder\u00e1 ver v\u00e1rios exemplos resolvidos da derivada da cossecante hiperb\u00f3lica. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante-hiperbolica\"><\/span> F\u00f3rmula para a derivada da cossecante hiperb\u00f3lica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A derivada da cossecante hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x vezes a cotangente hiperb\u00f3lica de x.<\/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-b2fef8fd91e2354a27e8902e390ddabf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x)\\cdot \\text{cotgh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"517\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, a <strong>derivada da cossecante hiperb\u00f3lica de uma fun\u00e7\u00e3o<\/strong> \u00e9 menos o produto da cossecante hiperb\u00f3lica da fun\u00e7\u00e3o vezes a cotangente hiperb\u00f3lica da fun\u00e7\u00e3o vezes a derivada da referida fun\u00e7\u00e3o.<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Resumindo, a f\u00f3rmula para derivar a cossecante de uma fun\u00e7\u00e3o \u00e9: <\/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-la-cosecante-hyperbolique.webp\" alt=\"derivado da cosecante hiperb\u00f3lica\" class=\"wp-image-2761\" width=\"505\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Na verdade, as duas express\u00f5es anteriores correspondem a uma \u00fanica f\u00f3rmula, a diferen\u00e7a \u00e9 que a regra da cadeia \u00e9 aplicada na segunda f\u00f3rmula. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante-hiperbolica\"><\/span> Exemplos de derivada da cossecante hiperb\u00f3lica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver qual \u00e9 a f\u00f3rmula da derivada da cossecante hiperb\u00f3lica, aqui est\u00e3o v\u00e1rios exemplos trabalhados desse tipo de derivada trigonom\u00e9trica.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<p> Neste primeiro exemplo, derivaremos a cossecante hiperb\u00f3lica de x ao quadrado:<\/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-24a7761cd3b41af2f9802ef84f616047_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o do argumento da cossecante hiperb\u00f3lica \u00e9 diferente de x, ent\u00e3o precisamos usar a f\u00f3rmula da derivada da cossecante hiperb\u00f3lica com a regra da cadeia.<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, para derivar essa fun\u00e7\u00e3o trigonom\u00e9trica, basta substituir os valores da f\u00f3rmula anterior, ou seja, no argumento da cossecante hiperb\u00f3lica e da tangente hiperb\u00f3lica, colocamos x <sup>2<\/sup> , e multiplicamos tudo pela derivada de x ao quadrado, que \u00e9 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-068551500cf0689b8d21dcb83f0b6bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x^2)\\cdot \\text{cotgh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"573\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<p> Neste exerc\u00edcio, veremos quanto \u00e9 a derivada da cossecante hiperb\u00f3lica de x ao cubo:<\/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-38165f7bf2e567bb8bab90ba80cf3c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para encontrar a derivada da cossecante hiperb\u00f3lica de uma fun\u00e7\u00e3o, aplicamos sua f\u00f3rmula:<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A derivada de x ao cubo \u00e9 3x <sup>2<\/sup> , ent\u00e3o a derivada de toda a fun\u00e7\u00e3o \u00e9: <\/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-b88f49530fdce04138277673f41d2457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x^3)\\cdot \\text{cotgh}(x^3)\\cdot 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"580\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste artigo explicamos como derivar a cossecante hiperb\u00f3lica de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea poder\u00e1 ver v\u00e1rios exemplos resolvidos da derivada da cossecante hiperb\u00f3lica. F\u00f3rmula para a derivada da cossecante hiperb\u00f3lica A derivada da cossecante hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x vezes a cotangente hiperb\u00f3lica de x. Portanto, a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivada-da-cossecante-hiperbolica\/\"> <span class=\"screen-reader-text\">Derivada da cossecante hiperb\u00f3lica<\/span> Leia mais &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":[11],"tags":[],"class_list":["post-395","post","type-post","status-publish","format-standard","hentry","category-derivados"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Derivada da cossecante hiperb\u00f3lica - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/derivada-da-cossecante-hiperbolica\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivada da cossecante hiperb\u00f3lica - Mathority\" \/>\n<meta property=\"og:description\" content=\"Neste artigo explicamos como derivar a cossecante hiperb\u00f3lica de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea poder\u00e1 ver v\u00e1rios exemplos resolvidos da derivada da cossecante hiperb\u00f3lica. F\u00f3rmula para a derivada da cossecante hiperb\u00f3lica A derivada da cossecante hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x vezes a cotangente hiperb\u00f3lica de x. 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Al\u00e9m disso, voc\u00ea poder\u00e1 ver v\u00e1rios exemplos resolvidos da derivada da cossecante hiperb\u00f3lica. F\u00f3rmula para a derivada da cossecante hiperb\u00f3lica A derivada da cossecante hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x vezes a cotangente hiperb\u00f3lica de x. 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