{"id":393,"date":"2023-07-03T04:31:43","date_gmt":"2023-07-03T04:31:43","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-arccosecant\/"},"modified":"2023-07-03T04:31:43","modified_gmt":"2023-07-03T04:31:43","slug":"turunan-arccosecant","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-arccosecant\/","title":{"rendered":"Turunan dari busur kosekan"},"content":{"rendered":"<p>Di halaman ini Anda akan melihat rumus turunan arccosecant. Selain itu, Anda akan dapat melihat latihan yang diselesaikan untuk turunan dari kosekan busur suatu fungsi. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-arcocosecante\"><\/span> Rumus turunan arccosecant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan arccosecant dari x adalah negatif satu perkalian x dengan akar x kuadrat dikurangi 1.<\/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-f0d7defc746af3a5f6f4f0c6b9032eb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{x\\cdot \\sqrt{x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, <strong>turunan arccosecant suatu fungsi<\/strong> sama dengan dikurangi hasil bagi turunan fungsi tersebut dibagi fungsi dikalikan akar fungsi tersebut kuadrat dikurangi satu.<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Faktanya, dua rumus sebelumnya sama, tetapi ekspresi kedua menerapkan aturan rantai. Faktanya, jika Anda mensubstitusi fungsi identitas x ke dalam u, Anda akan mendapatkan turunan arccosecant dari x karena turunan dari x adalah satu. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-derivee-de-larc-cosecant.webp\" alt=\"rumus turunan arccosecant\" class=\"wp-image-2734\" width=\"463\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Seperti yang telah Anda ketahui, arccosecan merupakan kebalikan dari fungsi trigonometri dari cosecan, namun turunannya sangat berbeda. Rumus fungsi trigonometri jenis lainnya ini dapat Anda lihat pada link berikut:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/berasal-dari-kosekan\/\">turunan dari kosekan<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocosecante\"><\/span> Contoh turunan busur kosekan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Melihat apa itu aturan turunan arccosecant, selanjutnya kita akan menyelesaikan dua contoh turunan jenis ini. Namun jika Anda masih memiliki pertanyaan tentang cara menurunkan busur kosekan, Anda dapat menanyakannya kepada kami di komentar.<\/p>\n<h3 class=\"wp-block-heading\" id=\"block-46cfc7df-b680-41c2-ad53-bd8a19834b32\"> Contoh 1<\/h3>\n<p> Dalam contoh ini, kita akan melihat berapa turunan dari kosekan busur dari fungsi kuadrat x <sup>2<\/sup> .<\/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-fca6065258c2a26d98bf6b5fb0eb4b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-2a112ce1-0dbe-43d5-95b3-4d8506c1a246\"> Untuk menghitung turunan arccosecant dari x kuadrat, kita menerapkan rumus yang kita lihat di atas: <\/p>\n<p class=\"has-text-align-center\" id=\"block-f73c7b5e-fb98-43c1-a3bb-52c9144eee8a\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-a4fe1876-f662-49c1-8d09-6a6c4b5528dd\"> Turunan x pangkat dua adalah 2x, jadi turunan fungsi gabungannya 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-eb4dcb62cafb03a267428465ac221f2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{x^2\\cdot \\sqrt{\\left(x^2\\right)^2-1}}=-\\cfrac{2x}{x^2\\cdot \\sqrt{x^4-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"582\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" id=\"block-1446420a-0d61-44d3-9e31-8c5935a432a7\"> Contoh 2<\/h3>\n<p> Dalam contoh kedua ini, kita akan menurunkan arccosecant dari suatu fungsi potensial.<\/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-8ef686c080851299fb2bf1960a042424_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(2x^3+9x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-0514a2ea-d85a-4b25-a7db-9c27533e7436\"> Kita perlu menggunakan aturan turunan arcsecant untuk mencari turunan seluruh fungsi.<\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-6abf3c5a-c400-48c6-8375-c05fcb255b20\"> Jadi, di pembilangnya kita tuliskan turunan dari argumen fungsi tersebut, dan di penyebutnya kita tulis ulang fungsi potensialnya dan kalikan dengan akar kuadrat dari fungsi argumen tersebut, kuadrat dikurangi 1:<\/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-ead8a1afc8e88458fea7abdab11ee836_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(2x^3+9x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{6x^2+9}{(2x^3+9x)\\cdot \\sqrt{\\left(2x^3+9x\\right)^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"582\" style=\"vertical-align: -30px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan melihat rumus turunan arccosecant. Selain itu, Anda akan dapat melihat latihan yang diselesaikan untuk turunan dari kosekan busur suatu fungsi. Rumus turunan arccosecant Turunan arccosecant dari x adalah negatif satu perkalian x dengan akar x kuadrat dikurangi 1. Oleh karena itu, turunan arccosecant suatu fungsi sama dengan dikurangi hasil bagi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-arccosecant\/\"> <span class=\"screen-reader-text\">Turunan dari busur 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-393","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 busur kosekan - 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\/turunan-arccosecant\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari busur kosekan - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan melihat rumus turunan arccosecant. Selain itu, Anda akan dapat melihat latihan yang diselesaikan untuk turunan dari kosekan busur suatu fungsi. Rumus turunan arccosecant Turunan arccosecant dari x adalah negatif satu perkalian x dengan akar x kuadrat dikurangi 1. 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