{"id":32,"date":"2023-09-17T11:02:19","date_gmt":"2023-09-17T11:02:19","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-arctangent-1\/"},"modified":"2023-09-17T11:02:19","modified_gmt":"2023-09-17T11:02:19","slug":"turunan-dari-arctangent-1","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-arctangent-1\/","title":{"rendered":"Turunan dari arctangent"},"content":{"rendered":"<p>Pada artikel ini, Anda akan mempelajari cara menurunkan arctangen suatu fungsi. Selain itu, Anda akan dapat melihat contoh turunan jenis ini dan bahkan berlatih dengan latihan yang diselesaikan pada turunan tangen busur. Terakhir, kami juga tunjukkan bukti rumus turunan tangen busur. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcotangente\"><\/span> Apa turunan dari garis singgung busur?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan dari garis singgung busur x adalah satu per satu ditambah x kuadrat.<\/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-cdeb5e29b862b8b9d5bc9f4c2c747106_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1+x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, <strong>turunan tangen suatu fungsi<\/strong> sama dengan hasil bagi turunan fungsi tersebut dibagi satu ditambah kuadrat 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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, fungsi tersebut diwakili oleh au, jadi ini akan menjadi rumus turunan dari tangen busur fungsi u. <\/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\/derivee-arctangente.webp\" alt=\"berasal dari garis singgung busur\" class=\"wp-image-1997\" width=\"389\" height=\"296\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat, rumus turunan invers tangen sangat mirip dengan rumus turunan arcsinus dan arccosine. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcotangente\"><\/span> Contoh turunan dari arctangent<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui rumus turunan tangen busur, kami akan menjelaskan turunan dari beberapa contoh turunan trigonometri jenis ini. Dengan cara ini, Anda akan lebih mudah memahami cara menurunkan arctangen suatu fungsi. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcotangente-de-2x\"><\/span> Contoh 1: Turunan dari arctangen 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-3c8877ac889f77baa22f66d4b2568418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kami menerapkan rumus untuk menyelesaikan turunannya:<\/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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Turunan dari 2x adalah 2, jadi turunan arctangen dari 2x adalah 2 per satu ditambah 2x 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-f2a5ff151a4471bb769c46ac896ee0ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{1+(2x)^2}}=\\cfrac{2}{1+ 4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"518\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcotangente-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari arctangen x kuadrat<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-3f62897c299972bd734ffe87b6d28e84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari hasil turunan dari contoh ini, kita perlu menggunakan rumus turunan tangen busur, yaitu:<\/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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Jadi, turunan fungsi x <sup>2<\/sup> adalah 2x, maka turunan tangen busur x yang dipangkatkan 2 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-4518d6b8df16464b2a763eb7d736504d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(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=\"507\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcotangente-del-seno-de-x\"><\/span> Contoh 3: Turunan dari arctangen sinus x<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-72df0a729eefc917694a84ecccd4a959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"170\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Logikanya, untuk menghitung turunannya Anda harus menerapkan rumus yang sesuai:<\/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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita mempunyai fungsi komposit, jadi kita harus menerapkan aturan rantai untuk menghitung turunan dari tangen busur: <\/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-f3897b362bb6b4681404918f45e91565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{\\text{cos}(x)}{1+\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"482\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcotangente\"><\/span> Latihan soal turunan dari garis singgung busur<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Turunkan fungsi arctangen 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-23cb449bba097b71c6154e6bfd755940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{arctan}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" 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-8ec295f2cfb72911775d2bc47d379e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\cfrac{\\text{arctan}(3x^4)}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"175\" 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-5e54c5dc5ee8464186009da410740df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\text{arctan}(x^5-3x^3+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"252\" 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-b63b4e04e749c7b7d4cfecca4391eee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arctan}^3(4x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" 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-6c72a415d8c2e54870c4dc2e92344cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arctan}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"185\" 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-4fad4c5f97c1492b8ad5df06b165d2c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{arctan}\\left(\\sqrt{x^2+2x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"227\" 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 solusinya<\/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-effa4065c7c98ae655b2cc5bdf14ca07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{3x^2}{1+\\left(x^3\\right)^2}=\\cfrac{3x^2}{1+x^6}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"235\" 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-2de05c8d708d379982abc8461f5d8706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{12x^3}{2\\left(1+\\left(3x^4\\right)^2\\right)}=\\cfrac{6x^3}{1+9x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"285\" style=\"vertical-align: -30px;\"><\/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-d72faae19f9b5cd7a8d53364bcf9817a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{5x^4-9x^2}{1+\\left(x^5-3x^3+10\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"248\" 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-ea7d5ff105b7432c2756cdcbf44e311b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=3\\text{arctan}^2(4x^2)\\cdot \\cfrac{8x}{1+\\left(4x^2\\right)^2}=\\cfrac{24x\\cdot\\text{arctan}^2(4x^2)}{1+16x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"453\" 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-6eefb865fce5124f8326d122437c3124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{\\cfrac{1}{x}}{1+\\bigl(\\ln(x)\\bigr)^2}=\\cfrac{1}{x\\left(1+\\ln^2(x)\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"315\" style=\"vertical-align: -23px;\"><\/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-6faff8aba659922b2cfc784a4f3dae4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{1}{1+\\left(\\sqrt{x^2+2x}\\right)^2}\\cdot \\cfrac{2x+2}{2\\sqrt{x^2+2x}}=\\cfrac{x+1}{\\left(1+x^2+2x\\right)\\sqrt{x^2+2x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"524\" style=\"vertical-align: -33px;\"><\/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-arcotangente\"><\/span>Demonstrasi rumus turunan garis singgung busur<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya kita akan membuktikan rumus turunan tangen busur.<\/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-88c05a50eddb183a57270676d6ebc5cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arctan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama-tama kita ubah garis singgung busur menjadi garis singgung dengan memanfaatkan fakta bahwa garis singgung busur adalah fungsi kebalikan dari garis singgung:<\/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-e806041dd9dbc7cf01bb34014aa18d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{tan}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kami membedakan kedua sisi persamaan:<\/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-ca9f080338b9ab014e272f81395146ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\cfrac{1}{\\text{cos}^2(y)}\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"114\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Kami menghapus dan&#8217;:<\/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-05c04d0ce365d8bd7848d4923038778c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\text{cos}^2(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Di sisi lain, berkat identitas trigonometri dasar kita mengetahui bahwa jumlah kuadrat sinus dan kosinus sama dengan 1. Oleh karena itu, kita dapat mengubah ekspresi sebelumnya menjadi pecahan:<\/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-34f7d2ec2a5836c843db8adea73d021f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" 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-d5314e15fe7e8ff7c9155906e7725483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\text{cos}^2(y)}{1}=\\cfrac{\\text{cos}^2(y)}{\\text{sen}^2(y)+\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"252\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Kami membagi semua suku dengan kuadrat kosinus:<\/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-39e03a87b9a62ab2db6a56192e44f531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"176\" style=\"vertical-align: -44px;\"><\/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-3cf88afedfff6a5c53ffb31df510b4ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"128\" style=\"vertical-align: -44px;\"><\/p>\n<\/p>\n<p> Sinus dibagi cosinus sama dengan garis singgung, jadi:<\/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-dbf6d65fa67f0a2161bd99ee7431f015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"124\" 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-db914ed4a068a6dff2598b981b1682d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{tan}^2(y)+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"126\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Seperti yang kita lihat di atas, garis singgung setara dengan variabel x, oleh karena itu kita dapat mensubstitusikan persamaan tersebut untuk mendapatkan rumus turunan dari garis singgung busur:<\/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-61292316edd6cef99a6135989713cd22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{x^2+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"88\" style=\"vertical-align: -14px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini, Anda akan mempelajari cara menurunkan arctangen suatu fungsi. Selain itu, Anda akan dapat melihat contoh turunan jenis ini dan bahkan berlatih dengan latihan yang diselesaikan pada turunan tangen busur. Terakhir, kami juga tunjukkan bukti rumus turunan tangen busur. Apa turunan dari garis singgung busur? Turunan dari garis singgung busur x adalah satu &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-arctangent-1\/\"> <span class=\"screen-reader-text\">Turunan dari arctangent<\/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-32","post","type-post","status-publish","format-standard","hentry","category-derivatif"],"yoast_head":"<!-- This site is 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