{"id":47,"date":"2023-09-17T10:54:18","date_gmt":"2023-09-17T10:54:18","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-kotangen\/"},"modified":"2023-09-17T10:54:18","modified_gmt":"2023-09-17T10:54:18","slug":"turunan-dari-kotangen","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-kotangen\/","title":{"rendered":"Turunan dari kotangen"},"content":{"rendered":"<p>Pada artikel ini, kita akan melihat cara menurunkan kotangen suatu fungsi. Anda akan menemukan contoh turunan kotangen dan latihan genap yang diselesaikan langkah demi langkah. Terakhir, kita buktikan rumus turunan kotangen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente\"><\/span> Rumus turunan kotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan kotangen x sama dengan negatif satu terhadap kuadrat sinus x.<\/strong> Turunan kotangen x juga sama dengan dikurangi kuadrat kosekan x, dan dikurangi jumlah satu ditambah kuadrat kotangen 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-0a3653f5c765d773ebc789107bf1a825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{1}{\\text{sen}^2(x)}=-\\text{cosec}^2(x)=-\\left(1+\\text{cotg}^2(x)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"393\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jika argumen kotangen adalah fungsi selain x, maka rumus turunan kotangen suatu fungsi sama dengan rumus sebelumnya, namun mengalikan ekspresi dengan turunan fungsi argumen tersebut.<\/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-38ea1d1edeaf5664c56a946b5a87577d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}=-u' \\cdot \\text{cosec}^2(u)=-u' \\cdot \\left(1+\\text{cotg}^2(u)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Artinya, ada tiga rumus berbeda untuk mencari turunan kotangen. Namun secara logika, ketiga rumus tersebut tidak harus menggunakan ketiga rumus tersebut, melainkan Anda bisa menurunkannya dengan rumus yang Anda sukai. <\/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-la-cotangente.webp\" alt=\"berasal dari kotangen\" class=\"wp-image-2685\" width=\"428\" height=\"361\" 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-cotangente\"><\/span> Contoh turunan kotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat rumus turunan kotangen suatu fungsi, pada bagian ini kita akan menyelesaikan beberapa contoh turunan trigonometri jenis ini. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cotangente-de-2x\"><\/span> Contoh 1: Turunan dari kotangen 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Dalam contoh ini kita akan melihat turunan kotangen dari fungsi 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-b95db136ea1e222c9f810d724216b083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Seperti yang telah kita lihat, untuk menghitung turunan kotangen Anda dapat menggunakan salah satu dari tiga rumus di atas. Dalam hal ini, kita akan menggunakan rumus sinusoidal:<\/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-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Karena 2x adalah suku derajat satu, maka turunannya adalah 2. Jadi turunan kotangen 2x adalah negatif dua dibagi kuadrat sinus 2x: <\/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-4151decbf7dd792fd0ea6aa6ca4b55f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"426\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cotangente-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari kotangen x kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Pada contoh kedua kita akan menentukan turunan dari kotangen 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-ec3733080f720a5115d2d6719d33d7e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam contoh ini, fungsi argumen kotangen bukanlah x, sehingga kita harus menerapkan aturan rantai untuk membedakan kotangen tersebut.<\/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-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Turunan x kuadrat adalah 2x, maka turunan kotangen x <sup>2<\/sup> adalah: <\/p>\n<p class=\"has-text-align-center\"><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-6aef87160d0da1da0b32e1e200f31b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cotangente-al-cubo\"><\/span> Contoh 3: Turunan dari kotangen pangkat tiga<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Terakhir, kita akan mengetahui berapa turunan kotangen pangkat tiga dari suatu fungsi polinomial:<\/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-9be8c3c10c50e3ef6bb701a11d3f46c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}^3(x^5-6x^2+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita mempunyai komposisi fungsi, jadi kita perlu menggunakan aturan rantai dengan rumus turunan suatu pangkat untuk mencari turunan kotangen: <\/p>\n<p class=\"has-text-align-center\"><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-ed0c6f314584b0f00021e3833de2b223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=-3\\cdot\\text{cotg}^2(x^5-6x^2+10)\\cdot\\frac{5x^4-12x}{\\text{sen}^2(x^5-6x^2+10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-cotangente\"><\/span> Latihan soal turunan kotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hitung turunan fungsi kotangen 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-e1e391853b53d81ed500fd590799cbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{cotg}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" 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-8581122adcd9d79db9862a27b57af0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{cotg}(2x^4+10x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" 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-e7814ccc95124c55f86b2f7036178254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=\\text{cotg}^5\\left(\\frac{x}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"160\" 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-1dcf8b02c8e9d9712210a78d116e2fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cotg}\\left(e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" 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-f358f9329696ee71ac2c1abfd5f9668e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{cotg}\\bigl(\\ln(x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"176\" 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-e26ae47cb88a301a3353d868fc9b74f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{cotg}\\left(\\sqrt{8x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"166\" 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>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-b002740b34952198a8284265a444cbed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=-\\cfrac{5}{\\text{sen}^2(5x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"171\" 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-d9b86f549fab91f93d0fc4e437e1c4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=-\\cfrac{8x+10}{\\text{sen}^2(2x^4+10x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" 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-eb1435fb7eb0c7bcff84741362417548_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)\\cdot \\left(-\\frac{1}{\\text{sen}^2\\left(\\frac{x}{2}\\right)}\\right)\\cdot \\frac{1}{2}=-\\frac{5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)}{2\\cdot \\text{sen}^2\\left(\\frac{x}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"468\" 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-4fb5fc0cea94ec46660b5bb16d9daaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-\\cfrac{2x\\cdot e^{x^2}}{\\text{sen}^2(e^{x^2})}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"175\" style=\"vertical-align: -18px;\"><\/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-efc6c63eb1a5cfc3f89deb4cfc3b4586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=-\\cfrac{\\cfrac{2x}{x^2}}{\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}=-\\cfrac{2}{x\\cdot\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"356\" 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-70d6c7ac291ee53490646ae841842eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-\\cfrac{\\frac{8}{2\\sqrt{8x}}}{\\text{sen}^2\\left(\\sqrt{8x}\\right)}=-\\cfrac{4}{\\sqrt{8x}\\cdot \\text{sen}^2\\left(\\sqrt{8x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"360\" style=\"vertical-align: -21px;\"><\/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-derivada-de-la-cotangente\"><\/span> Bukti turunan kotangen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pada bagian akhir ini, kita akan mendemonstrasikan rumus turunan kotangen. Untuk melakukannya, kita akan mulai dari definisi matematis fungsi kotangen, yang sama dengan kosinus dibagi 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-dd85e2f7ac86aa67c6bd2f82fedfa926_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}(x)=\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"131\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Sekarang kita membedakan fungsi tersebut dengan menerapkan aturan turunan suatu 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-0eb90358967efc64de6d45b8eabe5e37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{cotg}(x)\\bigr)'=\\left(\\frac{\\text{cos}(x)}{\\text{sen}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"181\" 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-7685acfe693a3c5e8dd2e543ad8ec7c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}(x)\\cdot \\text{sen}(x)-\\text{cos}(x)\\cdot \\text{cos}(x) }{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"349\" 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-9988024649ed4fdb4b1a9bb913aa813f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}^2(x)-\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"243\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Kita ambil faktor persekutuan sebagai penyebutnya dan hilangkan tanda negatif dari 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-b23352ad101cdc7e1adeb6316c6d66c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\bigl(\\text{sen}^2(x)+\\text{cos}^2(x)\\bigr)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"259\" 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-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Di sisi lain, kita tahu bahwa kuadrat sinus ditambah kuadrat kosinus sama dengan satu berkat identitas trigonometri dasar.<\/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-92d80771f891319379b2e756c5524aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(x)+\\text{cos}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" 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-dd14ec817754afcafd5d862afc0703b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{1}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"157\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dan dengan demikian kita memperoleh rumus pertama untuk turunan kotangen. Demikian pula kosekan merupakan kebalikan perkalian sinus, sehingga aturan kedua turunan kotangen juga terbukti:<\/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-41aafad77ef896612fe6851ee97d914a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\text{sec}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Terakhir, rumus ketiga turunan fungsi trigonometri ini dapat dibuktikan dengan mengubah pecahan dari langkah sebelumnya menjadi penjumlahan 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-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" 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-3780e44f1c85235473d47f418c7bc889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cotg}'(x)=-\\left(\\frac{\\text{sen}^2(x)}{\\text{sen}^2(x)}+\\frac{\\text{cos}^2(x)}{\\text{sen}^2(x)}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"266\" 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-e7a8b05807749ddd4b8979253dcb2f45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=-\\bigl(1+\\text{cotg}^2(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"200\" style=\"vertical-align: -7px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini, kita akan melihat cara menurunkan kotangen suatu fungsi. Anda akan menemukan contoh turunan kotangen dan latihan genap yang diselesaikan langkah demi langkah. Terakhir, kita buktikan rumus turunan kotangen. Rumus turunan kotangen Turunan kotangen x sama dengan negatif satu terhadap kuadrat sinus x. Turunan kotangen x juga sama dengan dikurangi kuadrat kosekan x, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-kotangen\/\"> <span class=\"screen-reader-text\">Turunan dari kotangen<\/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-47","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>\u25b7 Turunan kotangen (rumus dan contoh)<\/title>\n<meta name=\"description\" content=\"Cara menurunkan kotangen suatu fungsi (rumus). 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