{"id":394,"date":"2023-07-03T04:11:00","date_gmt":"2023-07-03T04:11:00","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-arctangen\/"},"modified":"2023-07-03T04:11:00","modified_gmt":"2023-07-03T04:11:00","slug":"turunan-dari-arctangen","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-arctangen\/","title":{"rendered":"Turunan dari arckotangen"},"content":{"rendered":"<p>Di sini Anda akan menemukan rumus turunan kotangen busur dan kami akan menjelaskan cara menurunkan kotangen busur suatu fungsi beserta contohnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-arcocotangente\"><\/span> rumus turunan arckotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong><strong>Turunan dari garis singgung busur x adalah negatif satu dibagi satu ditambah x kuadrat.<\/strong><\/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-50e6d74bd307289a24eb7f891974643f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{1+x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"424\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, <strong>turunan kotangen busur suatu fungsi<\/strong> sama dengan dikurangi turunan fungsi tersebut dibagi satu ditambah fungsi 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-e4a94f9fe1b97f77b028dfe2296debcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"424\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Perhatikan bahwa rumus pertama dan kedua sama, satu-satunya perbedaan adalah aturan rantai diterapkan pada ekspresi kedua. Faktanya, jika Anda mensubstitusikan x ke u, Anda akan mendapatkan rumus pertama karena turunan dari fungsi x adalah 1. <\/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\/derivee-de-larctangente.webp\" alt=\"berasal dari arckotangen\" class=\"wp-image-2747\" width=\"390\" height=\"281\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Meskipun kotangen busur merupakan fungsi kebalikan dari kotangen, turunannya sangat berbeda. Sebenarnya kotangen suatu fungsi memiliki tiga cara untuk menurunkannya, Anda bisa melihat semuanya di sini:<\/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-kotangen\/\">rumus turunan kotangen<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocotangente\"><\/span> Contoh turunan dari arckotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah melihat rumus turunan kotangen busur, berikut adalah dua soal penyelesaian turunan trigonometri jenis ini. Ingat juga bahwa jika Anda memiliki pertanyaan, Anda dapat meninggalkan pertanyaan Anda di bawah 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 kotangen 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-f643c789a6794a49d13eb08ba6a91fc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"145\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-2a112ce1-0dbe-43d5-95b3-4d8506c1a246\"> Pada argumen kotangen busur kita mempunyai fungsi selain x, sehingga kita perlu menerapkan rumus turunan kotangen busur 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-e4a94f9fe1b97f77b028dfe2296debcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"424\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p id=\"block-a4fe1876-f662-49c1-8d09-6a6c4b5528dd\"> Turunan dari x yang dipangkatkan menjadi dua adalah 2x, jadi pada pembilangnya kita harus memasukkan 2x dan pada penyebutnya fungsi dari argumen 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-eac3a555cca0fee987537eb7171a9145_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{1+(\\left(x^2\\right)^2}=-\\cfrac{2x}{1+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"548\" style=\"vertical-align: -20px;\"><\/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 kotangen busur dari fungsi polinomial derajat ketiga.<\/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-a62d6933c54de6f0c63f01a6edcaf0b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(x^3-9x+2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"216\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-0514a2ea-d85a-4b25-a7db-9c27533e7436\"> Kami menggunakan aturan turunan arckotangen untuk melakukan penurunannya:<\/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-e4a94f9fe1b97f77b028dfe2296debcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"424\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p id=\"block-6abf3c5a-c400-48c6-8375-c05fcb255b20\"> Jadi turunan arckotangen fungsi tersebut 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-634cbaeb640fd0886691ef88d12afc52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccotg}(x^3-9x+2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{3x^2-9}{1+(x^3-9x+2)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"596\" style=\"vertical-align: -17px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan rumus turunan kotangen busur dan kami akan menjelaskan cara menurunkan kotangen busur suatu fungsi beserta contohnya. rumus turunan arckotangen Turunan dari garis singgung busur x adalah negatif satu dibagi satu ditambah x kuadrat. Oleh karena itu, turunan kotangen busur suatu fungsi sama dengan dikurangi turunan fungsi tersebut dibagi satu ditambah &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-arctangen\/\"> <span class=\"screen-reader-text\">Turunan dari arckotangen<\/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-394","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 arckotangen - 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-dari-arctangen\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari arckotangen - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan rumus turunan kotangen busur dan kami akan menjelaskan cara menurunkan kotangen busur suatu fungsi beserta contohnya. rumus turunan arckotangen Turunan dari garis singgung busur x adalah negatif satu dibagi satu ditambah x kuadrat. 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