{"id":382,"date":"2023-07-03T18:53:21","date_gmt":"2023-07-03T18:53:21","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/"},"modified":"2023-07-03T18:53:21","modified_gmt":"2023-07-03T18:53:21","slug":"turunan-dari-fungsi-logaritma-logaritma-natural-neperian","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/","title":{"rendered":"Turunan dari fungsi logaritma"},"content":{"rendered":"<p>Di sini Anda akan menemukan cara menyelesaikan turunan fungsi logaritma dalam basis (rumus) apa pun. Selain itu, Anda juga dapat berlatih dengan latihan langkah demi langkah turunan fungsi logaritma.<\/p>\n<p> <strong>Rumus pembagian fungsi logaritma berbeda-beda tergantung apakah logaritma tersebut natural (dengan basis e) atau basis lain<\/strong> . Oleh karena itu, pertama-tama kita akan melihat kedua rumus tersebut secara terpisah beserta contoh untuk setiap kasus, lalu kita akan membuat ringkasan dari kedua aturan tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-un-logaritmo-natural-o-neperiano\"><\/span> Turunan dari logaritma natural atau natural<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan logaritma natural (atau logaritma natural) adalah hasil bagi turunan argumen logaritma dibagi fungsi argumen.<\/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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Logikanya, jika fungsi di dalam logaritma adalah fungsi identitas, maka pembilang turunannya tetap 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-1519db0b90e430fab54b04113c435118_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"331\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Perhatikan contoh penyelesaian turunan logaritma natural 3x 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-420e2f2cb107eb22019157bcb76c5645_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3}{3x}=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"384\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa logaritma natural adalah logaritma yang basisnya adalah bilangan e (bilangan Euler). <\/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-d5698ad2315473c75950453c15326f81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x)=\\log_e(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-un-logaritmo-en-base-a\"><\/span> Turunan dari logaritma berdasarkan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan logaritma ke basis apa pun sama dengan 1 dibagi dengan hasil kali x logaritma natural dari basis logaritma aslinya.<\/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-8b37542882d2bccf84707a3341af5813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi jika kita menerapkan aturan rantai, aturan turunan logaritmiknya 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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Misalnya turunan logaritma basis 2 dari x kuadrat 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-e934db01ce50b0ef6f597d5952637cfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_2(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{x^2\\cdot\\ln(2)}=\\cfrac{2}{x\\ln(2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"488\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-funcion-logaritmica\"><\/span> Rumus turunan fungsi logaritma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Mengingat pengertian turunan logaritma dan dua kemungkinan variannya, berikut rangkuman kedua rumus tersebut untuk memudahkan Anda mengingatnya. <\/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\/fonction-logarithmique-derivee.webp\" alt=\"turunan dari fungsi logaritma\" class=\"wp-image-1842\" width=\"395\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-funciones-logaritmicas\"><\/span> Memecahkan masalah turunan fungsi logaritma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Turunkan fungsi logaritma 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-8118283c3444e6c13b9aefdf0d8a11aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log(3x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/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-left\"> Dalam hal ini perlu untuk menyelesaikan turunan logaritma dalam basis desimal, oleh karena itu kita harus menerapkan rumus 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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, turunan logaritma basis 10 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-f340fe2c5f62e4f0c4499aca10845cf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log(3x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{6x}{3x^2\\cdot \\ln(10)}=\\cfrac{2}{x \\ln(10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"516\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ingatlah bahwa jika suatu logaritma tidak memiliki basis, berarti basisnya adalah 10.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 2<\/h3>\n<p> Turunkan logaritma natural (atau natural) 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-a44fc37965c07092cdfa5cb2679a8b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(x^3+4x^2\\right)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"165\" 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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Fungsi dalam soal ini adalah logaritma natural, jadi kita perlu menggunakan aturan berikut untuk menurunkan fungsi logaritma:<\/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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, turunan dari logaritma natural 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-fc06150c0093afdd84076e69171b7d38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{5\\left(x^3+4x^2\\right)^4\\cdot (3x^2+8x)}{\\left(x^3+4x^2\\right)^5}\\\\[2ex] &amp;=\\cfrac{5\\cdot (3x^2+8x)}{x^3+4x^2}\\\\[2ex] &amp;=\\cfrac{15x^2+40x}{x^3+4x^2}\\\\[2ex] &amp;=\\cfrac{15x+40}{x^2+4x}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"245\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Turunkan logaritma 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-5682f4fd6180c07879cfe9fb6a4b2583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_7(x^5+7x^2-3x+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"239\" style=\"vertical-align: -5px;\"><\/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-left\"> Dalam latihan ini kita perlu menurunkan logaritma basis 7, jadi kita akan menggunakan rumus 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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan turunan dari logaritmanya 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-182fbf09950c4930013d2f863888bdd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{5x^4+14x-3}{(x^5+7x^2-3x+1)\\cdot \\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"267\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Carilah turunan fungsi logaritma berikut dengan 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-218d7543ba82562bbf91b5f4e0ca3f1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\log_4\\left(\\frac{5x}{8x^2-1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/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-left\"> Untuk menyelesaikan turunan logaritma, pertama-tama kita dapat menyederhanakan fungsinya dengan menerapkan sifat-sifat logaritma:<\/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-2d0cedfe8d0bd4de138099938b10e39f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_4(5x)-\\log_4(8x^2-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita harus menggunakan rumus turunan logaritmik sebanyak dua kali, namun kedua turunan tersebut lebih mudah dihitung.<\/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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ringkasnya, turunan dari 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-85874bff9f3259727a78b50aece1f1e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{5}{5x\\cdot \\ln(4)}-\\cfrac{16x}{(8x^2-1)\\cdot \\ln(4)}\\\\[2ex]&amp;=\\cfrac{1}{x\\ln(4)}-\\cfrac{16x}{(8x^2-1)\\ln(4)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"279\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 5<\/h3>\n<p> Hitung turunan fungsi logaritma berikut dengan satu akar: <\/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-9518b9623edc80e9f5de230edb5e573c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(\\sqrt[4]{\\text{cos}(9x)}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"170\" 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-left\"> Pertama, kita akan menyederhanakan fungsinya menggunakan properti logaritma: <\/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-95cc0f73a05b0cde647035b17d0fed60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(\\text{cos}(9x)\\right)^{\\frac{1}{4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"154\" 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-fac1c4306bdc844dc069a28c995e5dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{1}{4}\\ln\\left(\\text{cos}(9x)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita menghilangkan radikal dari fungsinya, kita menggunakan aturan turunan dari logaritma natural atau natural:<\/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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, turunan dari fungsi logaritma komposit 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-440b871bd7321bb0121db9a588adde6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)&amp;=\\cfrac{1}{4}\\cdot \\cfrac{-\\text{sen}(9x)\\cdot 9}{\\text{cos}(9x)}=\\cfrac{-9\\text{sen}(9x)}{4\\text{cos}(9x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"304\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan cara menyelesaikan turunan fungsi logaritma dalam basis (rumus) apa pun. Selain itu, Anda juga dapat berlatih dengan latihan langkah demi langkah turunan fungsi logaritma. Rumus pembagian fungsi logaritma berbeda-beda tergantung apakah logaritma tersebut natural (dengan basis e) atau basis lain . Oleh karena itu, pertama-tama kita akan melihat kedua rumus &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\"> <span class=\"screen-reader-text\">Turunan dari fungsi logaritma<\/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-382","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 fungsi logaritma - 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-fungsi-logaritma-logaritma-natural-neperian\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari fungsi logaritma - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan cara menyelesaikan turunan fungsi logaritma dalam basis (rumus) apa pun. Selain itu, Anda juga dapat berlatih dengan latihan langkah demi langkah turunan fungsi logaritma. Rumus pembagian fungsi logaritma berbeda-beda tergantung apakah logaritma tersebut natural (dengan basis e) atau basis lain . Oleh karena itu, pertama-tama kita akan melihat kedua rumus &hellip; Turunan dari fungsi logaritma Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T18:53:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-491d95a8a33d226da4fc5d62a8e70f61_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\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari fungsi logaritma\",\"datePublished\":\"2023-07-03T18:53:21+00:00\",\"dateModified\":\"2023-07-03T18:53:21+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\"},\"wordCount\":390,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Derivatif\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-logaritma-logaritma-natural-neperian\/\",\"name\":\"Turunan dari fungsi logaritma - 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