{"id":391,"date":"2023-07-03T07:22:34","date_gmt":"2023-07-03T07:22:34","guid":{"rendered":"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/"},"modified":"2023-07-03T07:22:34","modified_gmt":"2023-07-03T07:22:34","slug":"berasal-dari-kosekan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/","title":{"rendered":"Turunan dari kosekan"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan kosekan suatu fungsi (rumus). Anda juga akan menemukan latihan yang diselesaikan selangkah demi selangkah untuk turunan kosekan. Dan terakhir, Anda akan dapat melihat demonstrasi rumus turunan trigonometri jenis ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante\"><\/span> Rumus turunan kosekan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan kosekan x sama dengan dikurangi hasil bagi kosinus x dibagi sinus kuadrat 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-19e966c85664331b8b6c87860849678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dengan menggunakan rumus trigonometri, kita juga dapat mendefinisikan turunan kosekan x sebagai dikurangi hasil kali kotangen x dikali kosekan 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-e66d4cc483a3f2c40401bf2e34fa54c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}=-\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\\cdot \\cfrac{1}{\\text{sen}(x)}=-\\text{cot}(x)\\cdot \\text{cosec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dan jika kita menerapkan aturan rantai, <strong>turunan kosekan suatu fungsi<\/strong> adalah dikurangi hasil kali turunan fungsi tersebut dikalikan kosinus dari fungsi tersebut, dibagi dengan sinus kuadrat dari fungsi tersebut.<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, rumus yang digunakan untuk menurunkan kosekan suatu fungsi adalah sebagai berikut: <\/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-formule-cosecante.webp\" alt=\"berasal dari rumus kosekan\" class=\"wp-image-2527\" width=\"398\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante\"><\/span> Contoh turunan dari kosekan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah mengetahui apa rumus turunan kosekan, sekarang kita akan memberikan beberapa contohnya. Jadi Anda bisa melihat dengan tepat bagaimana kosekan suatu fungsi diturunkan. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cosecante-de-2x\"><\/span> Contoh 1: Turunan dari kosekan 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Dalam contoh ini kita akan melihat berapa turunan dari kosekan 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-44aef07389e7b7d69f4ecf9e46660838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Fungsi argumen kosekan berbeda dengan x, sehingga kita perlu menggunakan aturan turunan kosekan dengan aturan rantai.<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi, untuk mencari turunan fungsi trigonometri ini, cukup substitusikan nilai pada rumus sebelumnya: pada argumen cosinus dan sinus kita masukkan 2x, dan u&#8217; sesuai dengan turunan dari 2x, yaitu 2: <\/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-8607025c53ca3c1a2c5e05e908d61bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2\\cdot \\text{cos}(2x)}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cosecante-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari kosekan x kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Pada latihan ini, kita akan melihat berapa turunan dari kosekan x kuadrat:<\/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-dc9de51c8f24850940b40de616428dd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logikanya, turunan fungsi trigonometri ini diselesaikan dengan menggunakan rumus turunan kosekan:<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Turunan x kuadrat menghasilkan 2x, jadi turunan kosekan x pangkat dua adalah: <\/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-0a6b69e1f9851904ec2fc68bffeedc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x\\cdot \\text{cos}(x^2)}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cosecante-al-cubo-de-una-funcion-exponencial\"><\/span> Contoh 3: Turunan kosekan pangkat tiga dari suatu fungsi eksponensial<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-8bd5c47e8cd53ab52d3d30f55f898490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}^3(e^{5x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Apapun argumen fungsi tersebut, aturan turunan kosekan suatu fungsi adalah:<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Namun dalam kasus ini kita mempunyai fungsi majemuk, karena kosekan dipangkatkan menjadi tiga dan terlebih lagi dalam argumennya terdapat fungsi eksponensial. Jadi, untuk membedakan seluruh fungsi, kita perlu menerapkan aturan rantai beberapa kali: <\/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-9ac2ce49dfcba1b7f27696dba0a2decb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle f'(x)&amp; = 3\\text{cosec}^2(e^{5x})\\cdot\\left(-\\frac{5e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\right)\\\\[1.5ex]&amp;=-\\frac{-15\\text{cosec}^2(e^{5x})\\cdot e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"316\" 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-la-cosecante\"><\/span> Menyelesaikan masalah turunan kosekan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Turunkan fungsi kosekan berikut: <\/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-9929e2437b0ed56c3510e3e0e66745c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{cosec}(x^4-2x^2)\" 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-90abcf0539f30dc6fc72414bfc74510f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{cosec}(x^3+e^x-10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"232\" 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-86a2ea6229cced9086f8baba7afd49dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cosec}\\bigl(\\ln(x^3+7x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" 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-45cdf124149223f4a3bec4984dc3ad3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{cosec}\\bigl(\\text{arccos}(x^7)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"217\" 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-45ae6ef998d8ab0c30309fe521b0bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{cosec}\\left(\\sqrt{9x^2-4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"226\" style=\"vertical-align: -11px;\"><\/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>lihat solusi<\/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-1fb207498fc67f62e6c30a0baecc9549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f('x)=-\\cfrac{(4x^3-4x)\\cdot \\text{cos}(x^4-2x^2)}{\\text{sen}^2(x^4-2x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"303\" style=\"vertical-align: -17px;\"><\/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-d42a3db78890f44f3cac95685ab9362e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f('x)=-\\cfrac{(3x^2+e^x)\\cdot \\text{cos}(x^3+e^x-10)}{\\text{sen}^2(x^3+e^x-10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"329\" style=\"vertical-align: -17px;\"><\/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-32dde68d2a11ef6a05d483b26f0a98ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp; =-\\cfrac{\\cfrac{3x^2+14x}{x^3+7x^2}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{\\cfrac{3x+14}{x^2+7x}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{(3x+14)\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{(x^2+7x)\\cdot \\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"333\" 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-b2bea25dae467cefdcc1bd48e8d9bc88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp; =-\\cfrac{-\\cfrac{7x^6}{\\sqrt{1-\\left(x^7\\right)^2}}\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =-\\cfrac{(-7x^6)\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =\\cfrac{7x^6\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"240\" width=\"348\" 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-eb70e1d7b6f2ce2636934b235904861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\text{E) }f'(x)&amp; =-\\cfrac{\\cfrac{18x-4}{2\\cdot\\sqrt{9x^2-4x}} \\cdot \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{\\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)}\\\\[1.5ex] &amp;=-\\cfrac{(18x-4)\\cdot  \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{2\\sqrt{9x^2-4x}\\cdot \\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"352\" 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-de-la-cosecante\"><\/span> Pembuktian rumus turunan kosekan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya kita akan mendemonstrasikan rumus turunan kosekan. Berbeda dengan demonstrasi lainnya, dalam hal ini kita tidak akan menggunakan limit yang mendefinisikan suatu turunan, tetapi kita akan mulai dari definisi matematis dari kosekan.<\/p>\n<p> Secara aljabar, fungsi trigonometri kosekan adalah kebalikan perkalian sinus:<\/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-6ac8ff987dcebfb971915b090d8dc455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x)=\\cfrac{1}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kita dapat mengambil turunan kosekan menggunakan aturan hasil bagi:<\/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-956e802336ed97943a839dbc059a168a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{0\\cdot \\text{sen}(x)-1\\cdot \\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"227\" style=\"vertical-align: -17px;\"><\/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-d26ab733704d285da0ec63f0901330b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Seperti yang Anda lihat, hanya dengan menerapkan aturan turunan suatu pembagian kita akan sampai pada rumus turunan kosekan. Dan karena turunan suatu hasil bagi sudah terbukti (bisa dilihat pada link berikut), maka aturan turunan kosekan juga sudah terbukti.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-hasil-bagi-pembagian\/\">bukti turunan suatu hasil bagi<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan kosekan suatu fungsi (rumus). Anda juga akan menemukan latihan yang diselesaikan selangkah demi selangkah untuk turunan kosekan. Dan terakhir, Anda akan dapat melihat demonstrasi rumus turunan trigonometri jenis ini. Rumus turunan kosekan Turunan kosekan x sama dengan dikurangi hasil bagi kosinus x dibagi sinus kuadrat x. Dengan menggunakan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\"> <span class=\"screen-reader-text\">Turunan dari kosekan<\/span> Selengkapnya &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":[38],"tags":[],"class_list":["post-391","post","type-post","status-publish","format-standard","hentry","category-derivatif"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Turunan dari cosecant - 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\/id\/berasal-dari-kosekan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari cosecant - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada artikel ini kami menjelaskan cara menurunkan kosekan suatu fungsi (rumus). Anda juga akan menemukan latihan yang diselesaikan selangkah demi selangkah untuk turunan kosekan. Dan terakhir, Anda akan dapat melihat demonstrasi rumus turunan trigonometri jenis ini. Rumus turunan kosekan Turunan kosekan x sama dengan dikurangi hasil bagi kosinus x dibagi sinus kuadrat x. Dengan menggunakan &hellip; Turunan dari kosekan Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T07:22:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19e966c85664331b8b6c87860849678d_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari kosekan\",\"datePublished\":\"2023-07-03T07:22:34+00:00\",\"dateModified\":\"2023-07-03T07:22:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\"},\"wordCount\":411,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Derivatif\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\",\"url\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\",\"name\":\"Turunan dari cosecant - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-07-03T07:22:34+00:00\",\"dateModified\":\"2023-07-03T07:22:34+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Turunan dari kosekan\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Turunan dari cosecant - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/","og_locale":"id_ID","og_type":"article","og_title":"Turunan dari cosecant - Mathority","og_description":"Pada artikel ini kami menjelaskan cara menurunkan kosekan suatu fungsi (rumus). 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