{"id":396,"date":"2023-07-03T02:36:56","date_gmt":"2023-07-03T02:36:56","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/"},"modified":"2023-07-03T02:36:56","modified_gmt":"2023-07-03T02:36:56","slug":"derivada-da-cotangente-hiperbolica","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/","title":{"rendered":"Derivada da cotangente hiperb\u00f3lica"},"content":{"rendered":"<p>Aqui explicamos como derivar a cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o. Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos da derivada da cotangente hiperb\u00f3lica. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente-hiperbolica\"><\/span> F\u00f3rmula para a derivada da cotangente hiperb\u00f3lica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A derivada da cotangente hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x ao quadrado.<\/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-159a0cc5b4ec54f5e5180986bf97e326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"439\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, a <strong>derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o<\/strong> \u00e9 menos a cossecante hiperb\u00f3lica da fun\u00e7\u00e3o vezes a derivada dessa fun\u00e7\u00e3o.<\/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-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Tenha em mente que na segunda f\u00f3rmula foi aplicada a regra da cadeia e esta f\u00f3rmula \u00e9 usada quando h\u00e1 uma fun\u00e7\u00e3o diferente de x no argumento da cotangente hiperb\u00f3lica. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-de-la-cotangente-hyperbolique.webp\" alt=\"derivado da cotangente hiperb\u00f3lica\" class=\"wp-image-2771\" width=\"456\" height=\"287\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Voc\u00ea pode encontrar em alguns livros de matem\u00e1tica que a derivada da cotangente \u00e9 outra, j\u00e1 que as tr\u00eas express\u00f5es a seguir s\u00e3o equivalentes:<\/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-6f9bb22138450fbc59797ea330d247b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\text{cosech}^2(x)=1-\\text{cotgh}^2(x)=-\\cfrac{1}{\\text{senh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"391\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Obviamente, voc\u00ea pode usar qualquer express\u00e3o que preferir entre as tr\u00eas para derivar a cotangente hiperb\u00f3lica, mas a mais usada \u00e9 a cossecante hiperb\u00f3lica ao quadrado. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cotangente-hiperbolica\"><\/span> Exemplos de derivada da cotangente hiperb\u00f3lica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de sabermos qual \u00e9 a f\u00f3rmula da derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o, resolveremos v\u00e1rios exemplos deste tipo de derivadas trigonom\u00e9tricas.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<p> Neste exemplo veremos qual \u00e9 a derivada da cotangente hiperb\u00f3lica da fun\u00e7\u00e3o 2x.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c7d3005851f13f7f239dbd5f976d87b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> No argumento da cotangente hiperb\u00f3lica temos uma fun\u00e7\u00e3o diferente de x, ent\u00e3o precisamos usar a f\u00f3rmula com a regra da cadeia para fazer a deriva\u00e7\u00e3o:<\/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-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Como 2x \u00e9 um termo de primeiro grau, sua derivada \u00e9 2. Portanto, para encontrar a derivada da cotangente hiperb\u00f3lica de 2x, simplesmente colocamos 2x no argumento ao quadrado da cossecante hiperb\u00f3lica e multiplicamos por 2.<\/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-d9805919c1591f35bad147992046725c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"478\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<p> No segundo exemplo, determinaremos o valor da derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o polinomial.<\/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-a861bc1c6734dac702da19a7f9614eb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(3x^4-5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Como vimos acima, a regra para derivar a cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o \u00e9 a seguinte:<\/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-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, a derivada da cotangente hiperb\u00f3lica deste exerc\u00edcio ser\u00e1 a seguinte:<\/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-0d9b5b922da23b4196f7ee1edd440f72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(3x^4-5x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(3x^4-5x)\\cdot(12x^3-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"582\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aqui explicamos como derivar a cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o. Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos da derivada da cotangente hiperb\u00f3lica. F\u00f3rmula para a derivada da cotangente hiperb\u00f3lica A derivada da cotangente hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x ao quadrado. Portanto, a derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o \u00e9 menos &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\"> <span class=\"screen-reader-text\">Derivada da cotangente 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-396","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 cotangente 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-cotangente-hiperbolica\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivada da cotangente hiperb\u00f3lica - Mathority\" \/>\n<meta property=\"og:description\" content=\"Aqui explicamos como derivar a cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o. Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos da derivada da cotangente hiperb\u00f3lica. F\u00f3rmula para a derivada da cotangente hiperb\u00f3lica A derivada da cotangente hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x ao quadrado. Portanto, a derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o \u00e9 menos &hellip; Derivada da cotangente hiperb\u00f3lica Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T02:36:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-159a0cc5b4ec54f5e5180986bf97e326_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Derivada da cotangente hiperb\u00f3lica\",\"datePublished\":\"2023-07-03T02:36:56+00:00\",\"dateModified\":\"2023-07-03T02:36:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\"},\"wordCount\":331,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Derivados\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\",\"url\":\"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/\",\"name\":\"Derivada da cotangente hiperb\u00f3lica - 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Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos da derivada da cotangente hiperb\u00f3lica. F\u00f3rmula para a derivada da cotangente hiperb\u00f3lica A derivada da cotangente hiperb\u00f3lica de x \u00e9 igual a menos a cossecante hiperb\u00f3lica de x ao quadrado. Portanto, a derivada da cotangente hiperb\u00f3lica de uma fun\u00e7\u00e3o \u00e9 menos &hellip; Derivada da cotangente hiperb\u00f3lica Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/","article_published_time":"2023-07-03T02:36:56+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-159a0cc5b4ec54f5e5180986bf97e326_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"2 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Derivada da cotangente hiperb\u00f3lica","datePublished":"2023-07-03T02:36:56+00:00","dateModified":"2023-07-03T02:36:56+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/"},"wordCount":331,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Derivados"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/","url":"https:\/\/mathority.org\/pt\/derivada-da-cotangente-hiperbolica\/","name":"Derivada da cotangente hiperb\u00f3lica - 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