{"id":382,"date":"2023-07-03T19:47:19","date_gmt":"2023-07-03T19:47:19","guid":{"rendered":"https:\/\/mathority.org\/it\/derivato-di-una-funzione-radicale-irrazionale\/"},"modified":"2023-07-03T19:47:19","modified_gmt":"2023-07-03T19:47:19","slug":"derivato-di-una-funzione-radicale-irrazionale","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/derivato-di-una-funzione-radicale-irrazionale\/","title":{"rendered":"Derivato da una radice"},"content":{"rendered":"<p>Qui spieghiamo come derivare una radice (o una funzione radicale). Troverai la formula per dividere le radici e gli esercizi risolti passo passo per le derivate delle radici. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-raiz\"><\/span> Formula per la derivata di una radice<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> La <strong>derivata di una radice,<\/strong> o funzione irrazionale, \u00e8 uguale alla derivata del radicando (espressione sotto il radicale) divisa per il prodotto dell&#8217;indice della radice per la radice stessa, sottraendo 1 dall&#8217;esponente del radicando.<\/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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Tuttavia, se il radicando radice \u00e8 solo una x, le formule si semplificano. La derivata radice di x \u00e8 quindi 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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> In breve, ci sono due formule per derivare una radice: la prima che pu\u00f2 essere usata sempre e la seconda che pu\u00f2 essere usata solo quando il radicando \u00e8 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\/derive-dune-racine.webp\" alt=\"derivato da una radice\" class=\"wp-image-1787\" width=\"361\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Se guardi da vicino, il termine al numeratore della frazione \u00e8 quello che risulta dall&#8217;applicazione della regola della catena quando si prende la derivata della radice. Questo \u00e8 il motivo per cui quando il radicando \u00e8 x, 1 appare al denominatore poich\u00e9 \u00e8 la derivata di x. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-raices\"><\/span> Esempi di derivati delle radici<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Data la formula per la derivata di una funzione radicale, di seguito spieghiamo alcuni esempi di questo tipo di derivata in modo che tu possa capire come derivare di una radice. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-raiz-cuadrada\"><\/span> Esempio 1: derivata di una radice quadrata<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Vedremo poi qual \u00e8 la derivata di una radice 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-12533a178fbfb7d1a6b3175d2a812cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> In questo caso, l&#8217;espressione all&#8217;interno della radice \u00e8 solo una x, quindi possiamo usare la seguente 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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Quindi la derivata di una radice quadrata \u00e8 uguale a 1 diviso per il prodotto di 2 volte la radice quadrata di x: <\/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-5e879d493e8b67755617d2aed1743cde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{2\\sqrt{x^{2-1}}}=\\cfrac{1}{2\\sqrt{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-raiz-cubica\"><\/span> Esempio 2: Derivazione di una radice cubica<span class=\"ez-toc-section-end\"><\/span><\/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-c3c5e7be9bc257eb2866277bae5be644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> In questo esempio, l&#8217;espressione sotto la radice \u00e8 una x, quindi possiamo applicare la seguente 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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Quindi la derivata di una radice cubica \u00e8 uguale a 1 diviso per 3 volte la radice cubica di x 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-f0e928affa231f99c8af7ebffb25049b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{3\\sqrt[3]{x^{3-1}}}=\\cfrac{1}{3\\sqrt[3]{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"436\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-raiz-cuarta\"><\/span> Esempio 3: Derivata di una radice quarta<span class=\"ez-toc-section-end\"><\/span><\/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-4a02a76ecccf5f654e0a9f7c3fb570e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ora non abbiamo una x sotto il segno radicale, ma abbiamo un&#8217;espressione algebrica pi\u00f9 complessa. Dobbiamo quindi utilizzare la formula generale per la derivata di una radice:<\/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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> L&#8217;espressione sotto il radicale \u00e8 una funzione di primo grado, quindi la sua derivata \u00e8 7. Pertanto, la derivata dell&#8217;intera funzione \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-d406850e42a532ebe3209ac6d705b0db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{7}{4\\sqrt[4]{(7x-2)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"446\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-raiz-dentro-de-otra\"><\/span> Esempio 4: Derivazione da una radice all&#8217;altra<span class=\"ez-toc-section-end\"><\/span><\/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-5955c2ba5e8301beb45ec4fe7207b601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x^2+\\sqrt[3]{x^4-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Per risolvere la derivata di questa radice composta da un&#8217;altra radice, dobbiamo applicare la seguente 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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> In questo caso, devi utilizzare la stessa formula due volte consecutive per calcolare la derivata: <\/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-c37131b50bda38022296c6401af727ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot\\left(x^2+\\sqrt[3]{x^4-5}\\right)' \\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot (x^4-5)'\\right)\\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot 4x^3\\right)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"211\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-raiz\"><\/span> Risolti problemi della derivata di una radice<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Calcolare le derivate delle seguenti radici: <\/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-3f3ee60a40f0696dc0b5ef1e5bda06ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\sqrt[5]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/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-e9589007466797e244646623ece04655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\sqrt[3]{x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" style=\"vertical-align: -5px;\"><\/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-983ef87ac1eca3d1e963de48bb867531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\sqrt{x^2-4x+9}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"189\" style=\"vertical-align: -5px;\"><\/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-24340e19537976608651d3554d8f47b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\sqrt[4]{x^9+5x^4-2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"207\" style=\"vertical-align: -5px;\"><\/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-4f82a43408b63e2399ec88e8a3e2e868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\sqrt[5]{3(x^2-1)^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"181\" style=\"vertical-align: -6px;\"><\/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-5280308e036830e09c0bdcd8bd8791fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\sqrt[6]{x^2+4(5x^3-8x)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"239\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>vedi soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-572ec9e7f3b912e18b40787ac9b212b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{1}{5\\sqrt[5]{x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"134\" style=\"vertical-align: -16px;\"><\/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-3bacf51d3e3fd8fa192f982456f2a8d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{4x^3}{3\\sqrt[3]{\\left(x^4\\right)^2}}= \\cfrac{4x^3}{3\\sqrt[3]{x^8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"225\" style=\"vertical-align: -30px;\"><\/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-3dbbfa5053cc4b46f21eee7a842a00c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{2x-4}{2\\sqrt{x^2-4x+9}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"204\" style=\"vertical-align: -16px;\"><\/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-5169c93bdfa2522a3219563eee1bb354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{9x^8+20x^3-2}{4\\sqrt[4]{\\left(x^9+5x^4-2x\\right)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"248\" style=\"vertical-align: -30px;\"><\/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-f68dce6e62d98d10d99daf57e0128069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{3\\cdot 4 \\cdot (x^2-1)^3\\cdot 2x}{5\\sqrt[5]{\\left(3\\left(x^2-1\\right)^4\\right)^4}}=\\cfrac{24x(x^2-1)^3}{5\\sqrt[5]{81\\left(x^2-1\\right)^{16}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"386\" style=\"vertical-align: -41px;\"><\/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-dd1d3bbced66caaed0ac254363e5f2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{2x+2\\cdot 4(5x^3-8x)\\cdot (15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}=\\cfrac{2x+8(5x^3-8x)(15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"571\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Qui spieghiamo come derivare una radice (o una funzione radicale). Troverai la formula per dividere le radici e gli esercizi risolti passo passo per le derivate delle radici. Formula per la derivata di una radice La derivata di una radice, o funzione irrazionale, \u00e8 uguale alla derivata del radicando (espressione sotto il radicale) divisa per &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/derivato-di-una-funzione-radicale-irrazionale\/\"> <span class=\"screen-reader-text\">Derivato da una radice<\/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-382","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 da una radice: 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\/derivato-di-una-funzione-radicale-irrazionale\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivato da una radice: Mathority\" \/>\n<meta property=\"og:description\" content=\"Qui spieghiamo come derivare una radice (o una funzione radicale). Troverai la formula per dividere le radici e gli esercizi risolti passo passo per le derivate delle radici. Formula per la derivata di una radice La derivata di una radice, o funzione irrazionale, \u00e8 uguale alla derivata del radicando (espressione sotto il radicale) divisa per &hellip; Derivato da una radice Leggi altro &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/it\/derivato-di-una-funzione-radicale-irrazionale\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T19:47:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d68fa956b939a4e9a483fc43509a3e5c_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=\"2 minuti\" \/>\n<script 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