{"id":382,"date":"2023-07-03T16:55:30","date_gmt":"2023-07-03T16:55:30","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivado-de-larcosina\/"},"modified":"2023-07-03T16:55:30","modified_gmt":"2023-07-03T16:55:30","slug":"derivado-de-larcosina","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivado-de-larcosina\/","title":{"rendered":"Derivada de arco seno"},"content":{"rendered":"<p>Neste artigo explicamos como derivar o arco seno de uma fun\u00e7\u00e3o. Voc\u00ea encontrar\u00e1 exemplos de derivadas do arco seno de fun\u00e7\u00f5es e poder\u00e1 at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. Por fim, voc\u00ea tamb\u00e9m ver\u00e1 a demonstra\u00e7\u00e3o da f\u00f3rmula da derivada do arco seno. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcoseno\"><\/span> Qual \u00e9 a derivada do arco seno?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A derivada do arco seno de x \u00e9 um sobre a raiz quadrada de um menos 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-924f0591661727fa46ea5f69bff39401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Portanto, a <strong>derivada do arco seno de uma fun\u00e7\u00e3o<\/strong> \u00e9 igual ao quociente da derivada dessa fun\u00e7\u00e3o dividido pela raiz quadrada de um menos a fun\u00e7\u00e3o 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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Logicamente, a segunda f\u00f3rmula \u00e9 obtida aplicando a regra da cadeia \u00e0 primeira f\u00f3rmula. <\/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-de-larcosine.webp\" alt=\"derivada de arco seno\" class=\"wp-image-1952\" width=\"403\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Lembre-se de que o arco seno \u00e9 a fun\u00e7\u00e3o inversa do seno, por isso tamb\u00e9m \u00e9 chamado de seno inverso. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcoseno\"><\/span> Exemplos de derivada de arco seno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver qual \u00e9 a f\u00f3rmula da derivada do arco seno, explicaremos v\u00e1rios exemplos deste tipo de derivadas trigonom\u00e9tricas. Dessa forma, ser\u00e1 mais f\u00e1cil entender como o arco seno de uma fun\u00e7\u00e3o \u00e9 derivado. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcoseno-de-2x\"><\/span> Exemplo 1: Derivada do arco seno de 2x<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-61368fb29b840d3583de92c8e6202006_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para encontrar a derivada da fun\u00e7\u00e3o arco seno, precisamos usar sua f\u00f3rmula correspondente:<\/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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Portanto, a derivada de 2x \u00e9 2, ent\u00e3o a derivada do arco seno de 2x \u00e9 2 dividido pela raiz de um menos 2x 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-b0282aa3f00df6b3bd1046fff94fa586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{\\sqrt{1-(2x)^2}}=\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"550\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcoseno-de-x-al-cuadrado\"><\/span> Exemplo 2: Derivada do arco seno de x ao quadrado<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-a4962743c0667c1443d315dd330bf3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Usamos a f\u00f3rmula da derivada do arco seno para deriv\u00e1-lo:<\/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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o x <sup>2<\/sup> \u00e9 de segundo grau, ent\u00e3o sua derivada \u00e9 2x. Assim, a derivada do arco seno de x elevado \u00e0 pot\u00eancia de 2 \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-60a677a7b7ca12bf048e6d20aca7b122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"538\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcoseno-de-ex\"><\/span> Exemplo 3: Derivada do arco seno de e <sup>x<\/sup><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-0843fbec2d0e53f9f16fd8e704af9763_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o neste exemplo \u00e9 uma fun\u00e7\u00e3o composta, ent\u00e3o precisamos aplicar a regra da cadeia para resolver 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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> A derivada de e <sup>x<\/sup> \u00e9 ela mesma, ent\u00e3o 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-e836cc1a00000f86d4f8891a12f4997d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{e^x}{\\sqrt{1-\\left(e^x\\right)^2}}=\\cfrac{e^x}{\\sqrt{1-e^{2x}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"542\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcoseno\"><\/span> Problemas resolvidos com derivada de arcoseno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Derive as seguintes fun\u00e7\u00f5es arco-seno: <\/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-515f2956c43c783ea330e8b3addf908c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arcsen}(6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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-537773e0ce262d3f14bb6af61b6d5d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arcsen}(x^2-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-d2ed0ca6a00694c6b35b651d9e206bbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arcsen}\\left(3x^4-6x^3+9+e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"304\" style=\"vertical-align: -11px;\"><\/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-c3b5ab58c98e35c39ea82368aebabded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arcsen}\\left(\\log_5(3x)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"212\" 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-25cafb754c9abd936852c9884fa1d9ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arcsen}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"182\" style=\"vertical-align: -7px;\"><\/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-3d8fcc06d1afecc77f744ddddafc702f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=\\cfrac{6}{\\sqrt{1-(6x)^2}}=\\cfrac{6}{\\sqrt{1-36x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"287\" style=\"vertical-align: -20px;\"><\/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-4491410567de31ccb0be97922264ca90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{2x-4}{\\sqrt{1-(x^2-4x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"219\" style=\"vertical-align: -20px;\"><\/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-b436dbd761b2261168c506e7e2e0d246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f'(x)=\\cfrac{12x^3-18x^2+2x\\cdot e^{x^2}}{\\sqrt{1-(3x^4-6x^3+9+e^{x^2})^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"311\" style=\"vertical-align: -21px;\"><\/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-57f2d6846bdde50321c1387f949d983a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{1}{\\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 5}=\\cfrac{1}{x\\cdot \\ln 5\\cdot \\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"519\" 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-0a82c0fd18a8672100ed3b79525a1028_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"253\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-arcoseno\"><\/span> Prova da f\u00f3rmula da derivada do arco seno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir, procedemos \u00e0 prova matem\u00e1tica da f\u00f3rmula da derivada do arco seno.<\/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-139a7a695d83cf004f32f983b10bde10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arcsen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Primeiro, transformamos o arco seno em seno:<\/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-443f95e83265d63f8d88d8782d014011_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{sen}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora diferenciamos ambos os lados da equa\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-1a653163fb7285dbfafcbaaa4b80031e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\text{cos}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> N\u00f3s limpamos voc\u00ea:<\/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-ac9839cbaf86cd3bcd2020ae70eb57e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{cos}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"86\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> A seguir, aplicamos a identidade trigonom\u00e9trica fundamental:<\/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-d5c5551414baf4b4a0f28a4eac057ae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{cos}(y)=\\sqrt{1-\\text{sen}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" 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-0535c541ff9c3a80c457aae33b359bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{1-\\text{sen}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> E, como deduzimos acima que x era equivalente ao seno de y, a igualdade permanece:<\/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-6fafe005791d06de3e64e76eda0ac194_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"103\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Como voc\u00ea pode ver, aplicando este procedimento obtivemos a f\u00f3rmula da derivada da fun\u00e7\u00e3o arco seno, portanto mostra-se que a f\u00f3rmula \u00e9 cumprida.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste artigo explicamos como derivar o arco seno de uma fun\u00e7\u00e3o. Voc\u00ea encontrar\u00e1 exemplos de derivadas do arco seno de fun\u00e7\u00f5es e poder\u00e1 at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. Por fim, voc\u00ea tamb\u00e9m ver\u00e1 a demonstra\u00e7\u00e3o da f\u00f3rmula da derivada do arco seno. Qual \u00e9 a derivada do arco seno? A derivada do &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivado-de-larcosina\/\"> <span class=\"screen-reader-text\">Derivada de arco seno<\/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-382","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 de Arcseno - 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\/derivado-de-larcosina\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivada de Arcseno - Mathority\" \/>\n<meta property=\"og:description\" content=\"Neste artigo explicamos como derivar o arco seno de uma fun\u00e7\u00e3o. Voc\u00ea encontrar\u00e1 exemplos de derivadas do arco seno de fun\u00e7\u00f5es e poder\u00e1 at\u00e9 praticar com exerc\u00edcios resolvidos passo a passo. Por fim, voc\u00ea tamb\u00e9m ver\u00e1 a demonstra\u00e7\u00e3o da f\u00f3rmula da derivada do arco seno. Qual \u00e9 a derivada do arco seno? 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