{"id":40,"date":"2023-09-17T10:58:44","date_gmt":"2023-09-17T10:58:44","guid":{"rendered":"https:\/\/mathority.org\/pt\/derivada-da-secante\/"},"modified":"2023-09-17T10:58:44","modified_gmt":"2023-09-17T10:58:44","slug":"derivada-da-secante","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/derivada-da-secante\/","title":{"rendered":"Derivada da secante"},"content":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 como derivar a secante de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exerc\u00edcios resolvidos passo a passo sobre a derivada da secante. E por fim, voc\u00ea encontrar\u00e1 a demonstra\u00e7\u00e3o da f\u00f3rmula desse tipo de derivada trigonom\u00e9trica. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-la-secante\"><\/span> Qual \u00e9 a derivada da secante?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A derivada da secante de x \u00e9 igual ao produto da secante de x pela tangente de x.<\/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-96448e16137a4b0d5cda8192ec339ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"434\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ao aplicar f\u00f3rmulas trigonom\u00e9tricas, a derivada da secante de x tamb\u00e9m pode ser definida como o quociente do seno de x dividido pelo quadrado do cosseno 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-7055796dc0e57b6284a41ca70ecca764_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)=\\cfrac{1}{\\text{cos}(x)}\\cdot \\cfrac{\\text{sen}(x)}{\\text{cos}(x)}=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"390\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> E se aplicarmos a regra da cadeia, a <strong>derivada da secante de uma fun\u00e7\u00e3o<\/strong> \u00e9 o produto da secante da fun\u00e7\u00e3o vezes a tangente da fun\u00e7\u00e3o vezes a derivada da fun\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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Em resumo, a f\u00f3rmula para a derivada da fun\u00e7\u00e3o secante \u00e9 a seguinte: <\/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-la-secante.webp\" alt=\"derivado da secante\" class=\"wp-image-2351\" width=\"475\" height=\"314\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-secante\"><\/span> Exemplos de derivada da secante<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos qual \u00e9 a f\u00f3rmula da derivada da secante, resolveremos v\u00e1rios exemplos deste tipo de derivadas trigonom\u00e9tricas. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-secante-de-2x\"><\/span> Exemplo 1: Derivada da secante de 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Neste exemplo veremos quanto vale a derivada da secante de 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-c8a3b19bc9ee15896b5416920d623745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para derivar a secante da fun\u00e7\u00e3o 2x, voc\u00ea deve usar sua f\u00f3rmula correspondente. Al\u00e9m disso, no argumento secante temos uma fun\u00e7\u00e3o diferente de x, portanto precisamos aplicar a regra da cadeia.<\/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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A fun\u00e7\u00e3o 2x \u00e9 linear, ent\u00e3o sua derivada \u00e9 2. Portanto, para encontrar a derivada, simplesmente substitu\u00edmos u por 2x e u&#8217; por 2 na 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-2decb8aff43ac88c25cae4f6c1443b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(2x)\\cdot \\text{tan}(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"482\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-secante-de-x-al-cuadrado\"><\/span> Exemplo 2: Derivada da secante de x ao quadrado<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Neste exerc\u00edcio veremos qual \u00e9 a derivada da secante 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-e1359b6d31f1ec6172c29ec2066b3fb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para derivar a secante de uma fun\u00e7\u00e3o voc\u00ea pode usar uma das duas f\u00f3rmulas vistas acima, mas neste caso iremos diferenciar a fun\u00e7\u00e3o com a f\u00f3rmula de multiplica\u00e7\u00e3o entre a secante e a tangente.<\/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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A derivada de x elevada \u00e0 pot\u00eancia de 2 d\u00e1 2x, ent\u00e3o a derivada da secante de x ao quadrado \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-2e0bdd83c01111c51620bd6a558a5930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x^2)\\cdot \\text{tan}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"490\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-secante-al-cubo-de-un-polinomio\"><\/span> Exemplo 3: Derivada do cubo secante de um polin\u00f4mio<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-6ee68247e5fd1854b875d655b1615701_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}^3(x^5+4x^2-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A regra para a derivada da secante de uma 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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Mas neste caso devemos derivar uma fun\u00e7\u00e3o composta, pois a secante \u00e9 elevada \u00e0 terceira pot\u00eancia e, al\u00e9m disso, em seu argumento temos uma fun\u00e7\u00e3o polinomial. Ent\u00e3o, para derivar toda a fun\u00e7\u00e3o, precisamos aplicar a regra da cadeia: <\/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-7ab88cc23ab3fb559e2386cd52637082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =3\\text{sec}^2(x^5+4x^2-3)\\text{sec}(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\\\[1.5ex]&amp;=3\\text{sec}^3(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"562\" 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-secante\"><\/span> Exerc\u00edcios resolvidos sobre a derivada de uma secante<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Derive as seguintes fun\u00e7\u00f5es secantes: <\/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-a63efa4ccc6266dc6db9552b5663ccb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"186\" 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-d4cd03385df118ead733c64d1524bb36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{sec}^4(5x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" 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-6b8e0ec036c5a0ccaca77d1116a2606a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"159\" 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-787d864c315ebf629c2505df13cfdf70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"178\" 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-1e9e9e0065335901bb018afd8458bf7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"187\" 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 a 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-c162c3a202d8d10ed26b6f5ad4afe7f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\\cdot \\text{tan}(x^6-6x^3)\\cdot (6x^5-18x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"415\" 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-72985d8bce95d808b9070bc7b834b271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{B) }f(x)&amp; =4\\text{sec}^3(5x^4)\\cdot \\text{sec}(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\\\[1.5ex] &amp;=4\\text{sec}^4(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"366\" 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-1a89fb7e8b228b31af9979a4fc0b08ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\\cdot \\text{tan}\\bigl(\\ln(x)\\bigr)\\cdot \\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"281\" style=\"vertical-align: -12px;\"><\/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-7a488bce8bdd2cb66ebb028ca017f172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\\cdot \\text{tan}\\left(e^{x^2+3x}\\right)\\cdot e^{x^2+3x}\\cdot (2x+3)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"429\" 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-b1bb860fafc464f3c8a30bf3e9b29a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\\cdot \\text{tan}\\left(\\sqrt{5x+1}\\right)\\cdot \\cfrac{5}{2\\sqrt{5x+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"400\" style=\"vertical-align: -16px;\"><\/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-de-la-secante\"><\/span> Demonstra\u00e7\u00e3o da f\u00f3rmula da derivada da secante<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir, provaremos a f\u00f3rmula da derivada da secante. Embora obviamente n\u00e3o seja necess\u00e1rio saber de cor a prova, \u00e9 sempre bom entender de onde v\u00eam as f\u00f3rmulas.<\/p>\n<p> Matematicamente, a defini\u00e7\u00e3o da secante \u00e9 o inverso multiplicativo do 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-8e3493c8e50b7c4b713b7c0f6ea9eca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x)=\\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"178\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Portanto, podemos tentar derivar a secante usando a regra do quociente:<\/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-37c02387c22125a313ff7fe65c1a7b37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"121\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> E, como vimos na primeira se\u00e7\u00e3o, a express\u00e3o anterior pode ser convertida na f\u00f3rmula da derivada da secante. Para fazer isso, separamos a fra\u00e7\u00e3o em duas fra\u00e7\u00f5es diferentes:<\/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-eb2f40cc564d430340271ea1b7659084_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> A divis\u00e3o do seno pelo cosseno equivale \u00e0 tangente, substitu\u00edmos portanto o referido quociente pela tangente:<\/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-3ce86a0b57ad6e2322c169eb90d9e8bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> De acordo com a defini\u00e7\u00e3o matem\u00e1tica da fun\u00e7\u00e3o secante, o cosseno \u00e9 o seu multiplicativo inverso. Ent\u00e3o, substituindo um dividido pelo cosseno pela secante, chegamos \u00e0 f\u00f3rmula da sua 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-d0ea3bb9b42cd0a3474363910fee95bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\text{sec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aqui voc\u00ea descobrir\u00e1 como derivar a secante de uma fun\u00e7\u00e3o. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exerc\u00edcios resolvidos passo a passo sobre a derivada da secante. E por fim, voc\u00ea encontrar\u00e1 a demonstra\u00e7\u00e3o da f\u00f3rmula desse tipo de derivada trigonom\u00e9trica. Qual \u00e9 a derivada da secante? A derivada da secante de x \u00e9 igual ao &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/derivada-da-secante\/\"> <span class=\"screen-reader-text\">Derivada da secante<\/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-40","post","type-post","status-publish","format-standard","hentry","category-derivados"],"yoast_head":"<!-- This site is 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