{"id":379,"date":"2023-07-03T19:47:19","date_gmt":"2023-07-03T19:47:19","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/"},"modified":"2023-07-03T19:47:19","modified_gmt":"2023-07-03T19:47:19","slug":"derivada-de-uma-funcao-raiz-irracional-radical","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/","title":{"rendered":"Derivado de uma raiz"},"content":{"rendered":"<p>Aqui explicamos como derivar uma raiz (ou uma fun\u00e7\u00e3o radical). Voc\u00ea encontrar\u00e1 a f\u00f3rmula de divis\u00e3o de ra\u00edzes e exerc\u00edcios resolvidos passo a passo para derivadas de ra\u00edzes. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-raiz\"><\/span> F\u00f3rmula para a derivada de uma raiz<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>derivada de uma raiz,<\/strong> ou fun\u00e7\u00e3o irracional, \u00e9 igual \u00e0 derivada do radicando (express\u00e3o abaixo do radical) dividida pelo produto do \u00edndice da raiz vezes a mesma raiz, subtraindo 1 do expoente do 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> No entanto, se o radicando raiz for apenas um x, as f\u00f3rmulas ser\u00e3o simplificadas. A derivada raiz de x \u00e9, portanto, 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-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> Resumindo, existem duas f\u00f3rmulas para derivar uma raiz: a primeira que sempre pode ser usada e a segunda que s\u00f3 pode ser usada quando o radicando for 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=\"derivado de uma raiz\" class=\"wp-image-1787\" width=\"361\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Se voc\u00ea olhar de perto, o termo no numerador da fra\u00e7\u00e3o \u00e9 aquele que resulta da aplica\u00e7\u00e3o da regra da cadeia ao calcular a derivada da raiz. \u00c9 por isso que quando o radicando \u00e9 x, 1 aparece no denominador, pois \u00e9 a derivada de x. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-raices\"><\/span> Exemplos de derivadas de raiz<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dada a f\u00f3rmula da derivada de uma fun\u00e7\u00e3o radical, explicamos a seguir v\u00e1rios exemplos desse tipo de derivada para que voc\u00ea entenda como derivar uma raiz. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-raiz-cuadrada\"><\/span> Exemplo 1: Derivada de uma raiz quadrada<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Veremos ent\u00e3o qual \u00e9 a derivada de uma raiz quadrada:<\/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> Neste caso, a express\u00e3o dentro da raiz \u00e9 apenas um x, ent\u00e3o podemos usar a seguinte f\u00f3rmula:<\/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> Portanto, a derivada de uma raiz quadrada \u00e9 igual a 1 dividido pelo produto de 2 vezes a raiz quadrada de 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> Exemplo 2: Derivada de uma raiz c\u00fabica<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> Neste exemplo, a express\u00e3o sob a raiz \u00e9 x, ent\u00e3o podemos aplicar a seguinte f\u00f3rmula:<\/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> Portanto, a derivada de uma raiz c\u00fabica \u00e9 igual a 1 dividido por 3 vezes a raiz c\u00fabica 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-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> Exemplo 3: Derivada de uma raiz 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> Agora n\u00e3o temos x sob o sinal radical, mas temos uma express\u00e3o alg\u00e9brica mais complexa. Portanto, devemos usar a f\u00f3rmula geral para a derivada de uma raiz:<\/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> A express\u00e3o sob o radical \u00e9 uma fun\u00e7\u00e3o de primeiro grau, ent\u00e3o sua derivada \u00e9 7. Assim, a derivada de toda a fun\u00e7\u00e3o \u00e9: <\/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> Exemplo 4: Deriva\u00e7\u00e3o de uma raiz para outra<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> Para resolver a derivada desta raiz composta por outra raiz, devemos aplicar a seguinte f\u00f3rmula:<\/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> Neste caso, voc\u00ea deve usar a mesma f\u00f3rmula duas vezes seguidas para calcular a derivada: <\/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> Problemas resolvidos da derivada de uma raiz<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Calcule as derivadas das seguintes ra\u00edzes: <\/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>veja solu\u00e7\u00e3o<\/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>Aqui explicamos como derivar uma raiz (ou uma fun\u00e7\u00e3o radical). Voc\u00ea encontrar\u00e1 a f\u00f3rmula de divis\u00e3o de ra\u00edzes e exerc\u00edcios resolvidos passo a passo para derivadas de ra\u00edzes. F\u00f3rmula para a derivada de uma raiz A derivada de uma raiz, ou fun\u00e7\u00e3o irracional, \u00e9 igual \u00e0 derivada do radicando (express\u00e3o abaixo do radical) dividida pelo &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\"> <span class=\"screen-reader-text\">Derivado de uma raiz<\/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-379","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>Derivado de uma raiz - 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-de-uma-funcao-raiz-irracional-radical\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivado de uma raiz - Mathority\" \/>\n<meta property=\"og:description\" content=\"Aqui explicamos como derivar uma raiz (ou uma fun\u00e7\u00e3o radical). Voc\u00ea encontrar\u00e1 a f\u00f3rmula de divis\u00e3o de ra\u00edzes e exerc\u00edcios resolvidos passo a passo para derivadas de ra\u00edzes. F\u00f3rmula para a derivada de uma raiz A derivada de uma raiz, ou fun\u00e7\u00e3o irracional, \u00e9 igual \u00e0 derivada do radicando (express\u00e3o abaixo do radical) dividida pelo &hellip; Derivado de uma raiz Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\" \/>\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=\"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-de-uma-funcao-raiz-irracional-radical\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Derivado de uma raiz\",\"datePublished\":\"2023-07-03T19:47:19+00:00\",\"dateModified\":\"2023-07-03T19:47:19+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\"},\"wordCount\":427,\"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-de-uma-funcao-raiz-irracional-radical\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\",\"url\":\"https:\/\/mathority.org\/pt\/derivada-de-uma-funcao-raiz-irracional-radical\/\",\"name\":\"Derivado de uma raiz - 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