{"id":400,"date":"2023-07-03T02:11:56","date_gmt":"2023-07-03T02:11:56","guid":{"rendered":"https:\/\/mathority.org\/it\/derivata-dellarcosecante-iperbolico\/"},"modified":"2023-07-03T02:11:56","modified_gmt":"2023-07-03T02:11:56","slug":"derivata-dellarcosecante-iperbolico","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/derivata-dellarcosecante-iperbolico\/","title":{"rendered":"Derivata dell&#39;arcosecante iperbolico"},"content":{"rendered":"<p>Qui troverai come calcolare la derivata dell&#8217;arcosecante iperbolico di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcosecante iperbolico. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-arcosecante-hiperbolica\"><\/span> Formula della derivata arcosecante iperbolica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>La derivata dell&#8217;arcosecante iperbolico di x \u00e8 uguale a meno 1 diviso per il prodotto di x per la radice di 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-30fd2d0fe7abd6d3774eaff22e8e762e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-1}{x\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Pertanto, la <strong>derivata dell&#8217;arcosecante iperbolico di una funzione<\/strong> \u00e8 meno la derivata di quella funzione divisa per il prodotto della funzione per la radice di uno meno la funzione quadrata.<\/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-12cb116a10cdca4bf5b49f2d06d69a58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> In breve, la formula per la derivata della funzione arcosecante iperbolica \u00e8: <\/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\/derive-de-larcosecant-hyperbolique.webp\" alt=\"derivato dall'arcosecante iperbolico\" class=\"wp-image-2786\" width=\"395\" height=\"281\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Entrambe le espressioni corrispondono in realt\u00e0 alla stessa formula, ma alla seconda formula viene applicata la regola della catena. Infatti, se sostituisci u con la funzione identit\u00e0 x, otterrai la prima formula poich\u00e9 la derivata di x \u00e8 1. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-arcosecante-hiperbolica\"><\/span> Esempi di derivata dell&#8217;arcosecante iperbolico<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dopo aver visto qual \u00e8 la formula per la derivata dell&#8217;arcosecante iperbolico, risolveremo due esercizi passo passo di questo tipo di derivate trigonometriche inverse. Quindi puoi vedere esattamente come derivare l&#8217;arcosecante iperbolico di una funzione.<\/p>\n<h3 class=\"wp-block-heading\"> Esempio 1<\/h3>\n<p> In questo esempio, determineremo qual \u00e8 la derivata dell&#8217;arcosecante iperbolico 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-a4e859277c6f50c7ea081153c8e79781_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Nell&#8217;argomento arcosecante iperbolico, abbiamo una funzione diversa da x, quindi dobbiamo utilizzare 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-12cb116a10cdca4bf5b49f2d06d69a58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> La funzione 2x \u00e8 lineare, quindi la sua derivata \u00e8 2. Pertanto, per trovare la derivata, sostituiamo semplicemente 2x con u e 2 con u&#8217; nella formula:<\/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-85f083f6c0009277265cca483ec04ac9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-2}{2x\\sqrt{1-(2x)^2}}=\\cfrac{-2}{2x\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"582\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Esempio 2<\/h3>\n<p> In questo secondo esercizio deriveremo l&#8217;arcosecante iperbolico di una funzione polinomiale:<\/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-0fc71b56d622872d79c469d74504f0fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(x^3-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> La funzione di questo esercizio \u00e8 composta, perch\u00e9 l&#8217;arcosecante iperbolico ha un&#8217;altra funzione nel suo argomento. Quindi dobbiamo usare la formula della derivata arcosecante iperbolica con la regola della catena per fare la sua derivazione:<\/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-12cb116a10cdca4bf5b49f2d06d69a58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Pertanto, al numeratore della frazione mettiamo la derivata della funzione polinomiale dell&#8217;argomento, e al denominatore cambiamo la u con la funzione polinomiale: <\/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-1f6389de5c7761fb5d35a9861156eec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f(x)=\\text{arcsech}(x^3-4x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}f'(x)&amp;=\\cfrac{-(3x^2-4)}{(x^3-4x)\\sqrt{1-(x^3-4x)^2}}\\\\[1.5ex] &amp;=\\cfrac{-3x^2+4}{(x^3-4x)\\sqrt{1-(x^3-4x)^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"117\" width=\"610\" style=\"vertical-align: 0px;\"><\/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-della-secante-iperbolica\/\">Derivata secante iperbolica<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivato-iperbolico-della-larcosina\/\">Derivato dell&#8217;arcoseno iperbolico<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-del-seno-iperbolico\/\">Derivata del seno iperbolico<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/deriva-dell\u2019arcosecante\/\">Derivato arcsecante<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivata-della-secante\/\">derivata della secante<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivato-della-larcosina\/\">derivato dell&#8217;arcoseno<\/a><\/span><\/li>\n<li> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/derivato-sinusale\/\">derivato dal seno<\/a><\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Qui troverai come calcolare la derivata dell&#8217;arcosecante iperbolico di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcosecante iperbolico. Formula della derivata arcosecante iperbolica La derivata dell&#8217;arcosecante iperbolico di x \u00e8 uguale a meno 1 diviso per il prodotto di x per la radice di uno meno x al quadrato. Pertanto, la derivata dell&#8217;arcosecante &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/derivata-dellarcosecante-iperbolico\/\"> <span class=\"screen-reader-text\">Derivata dell&#39;arcosecante iperbolico<\/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-400","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>Derivato dell&#039;arcosecante iperbolico - 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-dellarcosecante-iperbolico\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivato dell&#039;arcosecante iperbolico - Mathority\" \/>\n<meta property=\"og:description\" content=\"Qui troverai come calcolare la derivata dell&#8217;arcosecante iperbolico di una funzione. Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcosecante iperbolico. Formula della derivata arcosecante iperbolica La derivata dell&#8217;arcosecante iperbolico di x \u00e8 uguale a meno 1 diviso per il prodotto di x per la radice di uno meno x al quadrato. 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Inoltre, potrai vedere esempi risolti della derivata dell&#8217;arcosecante iperbolico. Formula della derivata arcosecante iperbolica La derivata dell&#8217;arcosecante iperbolico di x \u00e8 uguale a meno 1 diviso per il prodotto di x per la radice di uno meno x al quadrato. 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