{"id":402,"date":"2023-07-03T01:21:27","date_gmt":"2023-07-03T01:21:27","guid":{"rendered":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/"},"modified":"2023-07-03T01:21:27","modified_gmt":"2023-07-03T01:21:27","slug":"derivata-dellarcotangente-iperbolica","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/","title":{"rendered":"Derivata dell&#39;arcotangente iperbolica"},"content":{"rendered":"<p>In questo articolo spieghiamo come derivare l&#8217;arcotangente iperbolica di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcotangente iperbolica. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-arcocotangente-hiperbolica\"><\/span> Formula per la derivata dell&#8217;arcotangente iperbolica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>La derivata dell&#8217;arcotangente iperbolica di x \u00e8 uno su uno meno x al quadrato.<\/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-42f0b83c10ae509a0cda1aa4abf25b92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Pertanto, la <strong>derivata dell&#8217;arcotangente iperbolica di una funzione<\/strong> \u00e8 uguale al quoziente della derivata di quella funzione diviso per uno meno quella funzione al quadrato.<\/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-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Nota che la seconda formula \u00e8 come la prima ma applica la regola della catena, quindi potrebbero effettivamente essere considerate la stessa formula. <\/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-larccotangente-hyperbolique.webp\" alt=\"derivato dall'arcotangente iperbolica\" class=\"wp-image-2832\" width=\"391\" height=\"282\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> In alcuni libri di matematica potresti vedere che la derivata di questo tipo di funzione trigonometrica inversa \u00e8:<\/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-7c1e05f806ff6ead0b09d1af192c3345_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-1}{x^2-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"114\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Tuttavia, se guardi attentamente, sono la stessa formula, l&#8217;unica differenza \u00e8 che il numeratore e il denominatore della frazione sono stati moltiplicati per -1. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-arcocotangente-hiperbolica\"><\/span><meta charset=\"utf-8\"> Esempi di derivata dell&#8217;arcotangente iperbolica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Esempio 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-5885f3abf1d025a4716d0233fdd5efda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"147\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Nell&#8217;argomento dell&#8217;arcotangente iperbolico abbiamo una funzione diversa da x, quindi dobbiamo usare la formula della regola della catena per derivarla:<\/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-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> La derivata di 5x \u00e8 5, quindi metti 5 al numeratore della frazione e metti meno 5x al quadrato al denominatore:<\/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-36c2652240dffeccc7b2094f68c570c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(5x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{5}{1-(5x)^2}}=\\cfrac{5}{1- 25x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"535\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Esempio 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-4f6bb636493edeb7a8c2b9ee5e7890a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(e^{3x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Per risolvere la derivata di questa funzione, dobbiamo applicare la formula per la derivata dell&#8217;arcotangente iperbolica, che \u00e8 la seguente:<\/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-ccadba79123a5f5e81d2b777d5cb9ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"411\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> In questo caso abbiamo una funzione composta, poich\u00e9 nell&#8217;argomento della funzione trigonometrica \u00e8 presente una funzione esponenziale. Quindi dobbiamo usare la regola della catena per trovare la derivata dell&#8217;intera funzione: <\/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-32563dc460ac67e1fbb529d3485e8297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccoth}(e^{3x}) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3\\cdot e^{3x}}{1-\\left(e^{3x}\\right)^2}=\\cfrac{3e^{3x}}{1-3^{6x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"532\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"articulos-relacionados\"><\/span> Articoli simili<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolico\/\">Derivata dell&#8217;arcotangente iperbolico<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-della-tangente-iperbolica\/\">Derivata della tangente iperbolica<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-della-cotangente-iperbolica\/\">Derivata della cotangente iperbolica<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-dellarcotangente\/\">Derivato dell&#8217;arcotangente<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-1\/\">Derivata dell&#8217;arcotangente<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-della-cotangente\/\">derivato dalla cotangente<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-della-tangente\/\">derivata della tangente<\/a><\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In questo articolo spieghiamo come derivare l&#8217;arcotangente iperbolica di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcotangente iperbolica. Formula per la derivata dell&#8217;arcotangente iperbolica La derivata dell&#8217;arcotangente iperbolica di x \u00e8 uno su uno meno x al quadrato. Pertanto, la derivata dell&#8217;arcotangente iperbolica di una funzione \u00e8 uguale al quoziente della derivata di &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\"> <span class=\"screen-reader-text\">Derivata dell&#39;arcotangente iperbolica<\/span> Leggi altro &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-402","post","type-post","status-publish","format-standard","hentry","category-derivati"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Derivata dell&#039;arcotangente iperbolica - 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\/it\/derivata-dellarcotangente-iperbolica\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivata dell&#039;arcotangente iperbolica - Mathority\" \/>\n<meta property=\"og:description\" content=\"In questo articolo spieghiamo come derivare l&#8217;arcotangente iperbolica di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcotangente iperbolica. Formula per la derivata dell&#8217;arcotangente iperbolica La derivata dell&#8217;arcotangente iperbolica di x \u00e8 uno su uno meno x al quadrato. Pertanto, la derivata dell&#8217;arcotangente iperbolica di una funzione \u00e8 uguale al quoziente della derivata di &hellip; Derivata dell&#039;arcotangente iperbolica Leggi altro &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T01:21:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f0b83c10ae509a0cda1aa4abf25b92_l3.png\" \/>\n<meta name=\"author\" content=\"Squadra di Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Scritto da\" \/>\n\t<meta name=\"twitter:data1\" content=\"Squadra di Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo di lettura stimato\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\"},\"author\":{\"name\":\"Squadra di Mathority\",\"@id\":\"https:\/\/mathority.org\/it\/#\/schema\/person\/8d6f69ffbe48aea8b43675a9a3ddb9c8\"},\"headline\":\"Derivata dell&#39;arcotangente iperbolica\",\"datePublished\":\"2023-07-03T01:21:27+00:00\",\"dateModified\":\"2023-07-03T01:21:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\"},\"wordCount\":260,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/it\/#organization\"},\"articleSection\":[\"Derivati\"],\"inLanguage\":\"it-IT\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\",\"url\":\"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/\",\"name\":\"Derivata dell&#39;arcotangente iperbolica - 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Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcotangente iperbolica. Formula per la derivata dell&#8217;arcotangente iperbolica La derivata dell&#8217;arcotangente iperbolica di x \u00e8 uno su uno meno x al quadrato. Pertanto, la derivata dell&#8217;arcotangente iperbolica di una funzione \u00e8 uguale al quoziente della derivata di &hellip; Derivata dell&#39;arcotangente iperbolica Leggi altro &raquo;","og_url":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/","article_published_time":"2023-07-03T01:21:27+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42f0b83c10ae509a0cda1aa4abf25b92_l3.png"}],"author":"Squadra di Mathority","twitter_card":"summary_large_image","twitter_misc":{"Scritto da":"Squadra di Mathority","Tempo di lettura stimato":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/"},"author":{"name":"Squadra di Mathority","@id":"https:\/\/mathority.org\/it\/#\/schema\/person\/8d6f69ffbe48aea8b43675a9a3ddb9c8"},"headline":"Derivata dell&#39;arcotangente iperbolica","datePublished":"2023-07-03T01:21:27+00:00","dateModified":"2023-07-03T01:21:27+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/"},"wordCount":260,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/it\/#organization"},"articleSection":["Derivati"],"inLanguage":"it-IT","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/","url":"https:\/\/mathority.org\/it\/derivata-dellarcotangente-iperbolica\/","name":"Derivata dell&#39;arcotangente iperbolica - 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