{"id":383,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivado-de-larcosina-2\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"derivado-de-larcosina-2","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivado-de-larcosina-2\/","title":{"rendered":"Derivada do arco cosseno"},"content":{"rendered":"<p>Aqui explicamos como derivar o arco cosseno de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos de derivadas do arco cosseno e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. Finalmente, mostramos a prova da f\u00f3rmula da derivada do arco cosseno. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span> Qual \u00e9 a derivada do arco cosseno?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A derivada do arco cosseno de x \u00e9 menos 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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Portanto, a <strong>derivada do arco cosseno de uma fun\u00e7\u00e3o<\/strong> \u00e9 igual a menos o quociente da derivada dessa fun\u00e7\u00e3o dividido pela raiz quadrada de um menos essa fun\u00e7\u00e3o 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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Na verdade, a primeira f\u00f3rmula \u00e9 obtida substituindo x por u na segunda f\u00f3rmula. Ent\u00e3o, para recapitular, a f\u00f3rmula para a derivada do cosseno inverso \u00e9: <\/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-arc-cosinus.webp\" alt=\"derivada de arco cosseno\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Como voc\u00ea pode ver, a f\u00f3rmula da derivada do arco cosseno \u00e9 como a<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/derivado-de-larcosina\/\">derivada do arco seno<\/a><\/span> , mas adicionando um negativo antes dela. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span> Exemplos da derivada do arco cosseno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dada a f\u00f3rmula da derivada da fun\u00e7\u00e3o arcocosseno, analisaremos agora v\u00e1rios exemplos deste tipo de derivadas trigonom\u00e9tricas. Dessa forma, ser\u00e1 mais f\u00e1cil entender como o arco cosseno de uma fun\u00e7\u00e3o \u00e9 derivado. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcocoseno-de-2x\"><\/span> Exemplo 1: Derivada do arco cosseno 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-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para resolver a derivada do arco cosseno, usamos sua 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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> A derivada de 2x \u00e9 2, ent\u00e3o a derivada do arco cosseno de 2x \u00e9 menos 2 sobre a 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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"576\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span> Exemplo 2: Derivada do arco cosseno 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-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Aplicamos a f\u00f3rmula da derivada do arco cosseno com a regra da cadeia 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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Como a derivada da fun\u00e7\u00e3o x <sup>2<\/sup> \u00e9 2x, a derivada do arco cosseno de x elevado a 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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"565\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcocoseno-de-un-logaritmo\"><\/span> Exemplo 3: Derivada do arco cosseno de um logaritmo<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-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o neste exemplo \u00e9 uma fun\u00e7\u00e3o composta por um arco cosseno e um logaritmo natural, por isso precisamos de utilizar a regra da cadeia para deriv\u00e1-la.<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> A derivada do logaritmo natural \u00e9 dividida por x, portanto a derivada da fun\u00e7\u00e3o inteira \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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" 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-arcocoseno\"><\/span> Derivada de arcoseno resolveu problemas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Derive as seguintes fun\u00e7\u00f5es arcosseno: <\/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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" style=\"vertical-align: -7px;\"><\/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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" style=\"vertical-align: -7px;\"><\/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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" 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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" 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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" 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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" style=\"vertical-align: 0px;\"><\/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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" style=\"vertical-align: 0px;\"><\/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-d1a362c38a56084dec3c6ebbccba9ab0_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=\"267\" 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-arcocoseno\"><\/span> Prova da f\u00f3rmula da derivada do arco cosseno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nesta se\u00e7\u00e3o, demonstraremos a f\u00f3rmula da derivada do arco cosseno.<\/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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Primeiro, transformamos o arco cosseno em cosseno:<\/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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Deduzimos agora os dois lados da igualdade:<\/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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" 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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Usamos a identidade trigonom\u00e9trica fundamental para transformar seno em cosseno:<\/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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Mas acima deduzimos que x \u00e9 igual ao cosseno de y, ent\u00e3o a equa\u00e7\u00e3o 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-8c3b21ba43e58ec763ab27498aa4fb92_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=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> E assim chegamos \u00e0 express\u00e3o para a derivada do arco cosseno, ent\u00e3o sua f\u00f3rmula est\u00e1 demonstrada.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aqui explicamos como derivar o arco cosseno de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos de derivadas do arco cosseno e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. Finalmente, mostramos a prova da f\u00f3rmula da derivada do arco cosseno. Qual \u00e9 a derivada do arco cosseno? A derivada do arco cosseno de x \u00e9 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivado-de-larcosina-2\/\"> <span class=\"screen-reader-text\">Derivada do arco cosseno<\/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-383","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 do arco cosseno - 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-2\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivada do arco cosseno - Mathority\" \/>\n<meta property=\"og:description\" content=\"Aqui explicamos como derivar o arco cosseno de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea encontrar\u00e1 exemplos de derivadas do arco cosseno e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. Finalmente, mostramos a prova da f\u00f3rmula da derivada do arco cosseno. Qual \u00e9 a derivada do arco cosseno? 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