{"id":35,"date":"2023-09-17T11:01:09","date_gmt":"2023-09-17T11:01:09","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/"},"modified":"2023-09-17T11:01:09","modified_gmt":"2023-09-17T11:01:09","slug":"turunan-dari-hasil-perkalian","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/","title":{"rendered":"Turunan dari suatu produk (atau perkalian)"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan hasil kali dua fungsi (rumus). Selain itu, Anda juga dapat melihat beberapa contoh turunan perkalian fungsi dan bahkan berlatih menyelesaikan soal turunan perkalian. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-un-producto\"><\/span> Rumus turunan suatu produk<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan suatu hasil kali dua fungsi yang berbeda sama dengan hasil kali turunan fungsi pertama dengan fungsi kedua yang tidak terdiferensiasi ditambah hasil kali fungsi pertama yang tidak terdiferensiasi dengan turunan fungsi kedua.<\/strong><\/p>\n<p> Dengan kata lain, jika <em>f(x)<\/em> dan <em>g(x)<\/em> merupakan dua fungsi yang berbeda, maka rumus turunan perkalian kedua fungsi tersebut adalah sebagai berikut: <\/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\/derive-dun-produit.webp\" alt=\"berasal dari suatu produk\" class=\"wp-image-2103\" width=\"318\" height=\"298\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Jadi, dengan menerapkan aturan turunan suatu produk, kita beralih dari perkalian sederhana ke dua produk berbeda. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-un-producto\"><\/span> Contoh turunan suatu produk<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui rumus turunan suatu hasil kali (atau perkalian), kita akan menyelesaikan beberapa contoh turunan jenis ini. Ini akan memudahkan Anda memahami bagaimana hasil kali dua fungsi diturunkan.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 1<\/h3>\n<p> Dalam contoh ini kita akan menyelesaikan turunan dua fungsi potensial dengan mengalikan:<\/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-ac06a60a36e2b2b8b42a4e84aae6d78f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5x^2\\cdot (x^3+4x-6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Seperti yang kita lihat pada bagian sebelumnya, rumus turunan perkalian 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-775fe6e5ac196e5a44c840866e35062d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)\\cdot g(x) \\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"252\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, pertama-tama kita harus menghitung turunan masing-masing fungsi secara terpisah: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-39\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f6ba571ede98526688967d6db6b708d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 5x^2=10x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"104\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81f76a053e0ede02d46b917b5733f0cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^3+4x-6)=3x^2+4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"209\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Dan setelah kita mengetahui turunan setiap fungsi, kita bisa menerapkan rumus turunan hasil kali dua fungsi. Artinya, kita mengalikan turunan faktor pertama dengan faktor kedua tanpa membedakan, lalu menjumlahkan hasil kali faktor pertama tanpa membedakan dengan turunan faktor kedua:<\/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-00f424cf1f72c1d3822c14d49873253e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=5x^2\\cdot (x^3+4x-6)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=10x\\cdot (x^3+4x-6)+5x^2\\cdot (3x^2+4)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"87\" width=\"338\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Terakhir, kami melakukan operasi untuk menyederhanakan hasil yang diperoleh:<\/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-48b8d455b68b87932ca3a437f5ffe3a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =10x\\cdot (x^3+4x-6)+5x^2\\cdot (3x^2+4)\\\\[1.5ex] &amp; = 10x^4+40x^2-60x +15x^4+20x^2 \\\\[1.5ex] &amp; = 25x^4+60x^2-60x\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"338\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 2<\/h3>\n<p> Dalam hal ini kita akan menurunkan hasil kali konstanta dengan suatu 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-0eac27878f19facde1912b0e4c80f7c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=7\\cdot (x^2+3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Aturan turunan suatu produk adalah sebagai 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-775fe6e5ac196e5a44c840866e35062d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)\\cdot g(x) \\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"252\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jadi, kami secara terpisah menurunkan setiap fungsi yang merupakan bagian dari produk: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-42\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e80b2c2aeed333ee755f36592771ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ce4329169c51d065b3eaa2539afa18d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^2+3x)=2x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Lalu kita terapkan aturan turunan perkalian:<\/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-6c2d81edaa002aeb66ca6eec22bec001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=7\\cdot (x^2+3x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=0\\cdot (x^2+3x)+7\\cdot (2x+3)=14x+21\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"87\" width=\"353\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Perhatikan bahwa turunan suatu konstanta selalu nol, sehingga kita dapat menyimpulkan bahwa <strong>turunan dari perkalian suatu konstanta dengan suatu fungsi sama dengan hasil kali konstanta dan turunan fungsi tersebut.<\/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-df912584fe52a7417fef5fa910376453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}z(x)=k\\cdot f(x) \\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=k\\cdot f'(x)\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 3<\/h3>\n<p> Mari kita selesaikan hasil kali antara fungsi eksponensial dan logaritma 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-e835022b92bf8922fece3bfff5b0fe79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{3x}\\cdot \\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus turunan perkalian dua fungsi 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-775fe6e5ac196e5a44c840866e35062d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)\\cdot g(x) \\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"252\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kita harus terlebih dahulu membuat turunan masing-masing fungsi yang membentuk hasil perkaliannya secara terpisah, yaitu sebagai berikut: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-45\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8bd255b76b5292f44a9af4bda726a928_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 4^{3x}=4^{3x}\\cdot \\ln (4) \\cdot 3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"169\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5e20aacbfc682c8afa58940cf8306f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\ln(x^2)=\\cfrac{2x}{x^2}=\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"156\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Oleh karena itu, hasil kali turunan dari fungsi-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-9e1cb417a69252fe05883f7963bcb8db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=4^{3x}\\cdot \\ln(x^2)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=4^{3x}\\cdot \\ln (4) \\cdot 3\\cdot \\ln(x^2) +4^{3x}\\cdot \\cfrac{2}{x} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"290\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-un-producto\"><\/span> Latihan soal turunan suatu produk<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Turunkan produk fungsi 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-67f07c0bd975c646a55e36e71cf4a4c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=5\\ln(3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" 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-d8a0c3d9bc420193e3c1990868382d3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=(4x^2+1)(6x^3-7)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"225\" 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-61bc2db7b665db51e7467b0084d16de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cos}(4x)\\cdot e^{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"175\" 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-c6e9fe99ab311488946ed15068a12ea6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=(3x^3-4x^2+8x)\\cdot \\sqrt{6x^2+3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"310\" 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-88a563e417f4c63f256a599945356dd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=5^{4x}\\cdot \\log_9(x^3-x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"213\" 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-aa9abf01257a07e3610d58665ff5a149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=\\left(10x^6-6x^5\\right)^4\\cdot \\text{arcsen}(x^2+9x)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"323\" 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-a2b0cfd5d2fab9c30534aaf5a8873bba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=5\\cdot \\cfrac{3}{3x} =\\cfrac{5}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"168\" 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-f46e303cda3be6c3781f7ee4c46c1680_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{B) }f'(x)&amp;=8x\\cdot (6x^3-7)+(4x^2+1)\\cdot 18x^2\\\\[1.2ex]&amp;=48x^4-56x+72x^4+18x^2\\\\[1.2ex]&amp;=120x^4+18x^2-56x \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"331\" style=\"vertical-align: 0px;\"><\/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-1ee37a1f2ba1f12185bf7ea63668b7cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f'(x) =-4\\text{sen}(4x)\\cdot e^{x^2}+\\text{cos}(4x)\\cdot e^{x^2}\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"351\" 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-384d51cd4aff14037124c89ca3f77ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=(9x^2-8x+8)\\cdot \\sqrt{6x^2+3x}+(3x^3-4x^2+8x)\\cdot\\cfrac{12x+3}{2\\sqrt{6x^2+3x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"553\" style=\"vertical-align: -16px;\"><\/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-88020b03c9d895b81bf29a7cdeda7528_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f'(x)=5^{4x}\\cdot \\ln(5) \\cdot 4 \\cdot \\log_9(x^3-x)+ 5^{4x}\\cdot\\cfrac{3x^2-1}{(x^3-x)\\ln(9)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"455\" 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-5dbaa6f333ff27c717b6478d26154025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }f'(x)=&amp; 4\\left(10x^6-6x^5\\right)^3\\cdot (60x^5-30x^4)\\cdot \\text{arcsen}(x^2+9x)\\ +\\\\[1.2ex] &amp;+\\left(10x^6-6x^5\\right)^4\\cdot \\cfrac{2x+9}{\\sqrt{1-\\left(x^2+9x\\right)^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"473\" style=\"vertical-align: 0px;\"><\/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=\"derivada-de-un-producto-de-tres-funciones\"><\/span> Berasal dari produk tiga fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya, kami tinggalkan rumus turunan dari perkalian 3 fungsi, karena rumus ini sangat mirip dengan rumus 2 fungsi dan dapat berguna dalam beberapa kasus.<\/p>\n<p> <strong>Turunan suatu hasil kali tiga fungsi<\/strong> sama dengan hasil kali turunan fungsi pertama dan dua fungsi lainnya, ditambah hasil kali turunan fungsi kedua dan dua fungsi lainnya, ditambah hasil kali turunan fungsi tersebut. fungsi ketiga.fungsi dengan dua fungsi lainnya.<\/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-ab98569b058580b87eb57088447f4f49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=1mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}z(x)=f(x)\\cdot g(x)\\cdot h(x) \\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=f'(x)\\cdot g(x)\\cdot h(x)+f(x)\\cdot g'(x)\\cdot h(x)+f(x)\\cdot g(x)\\cdot h'(x)\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Misalnya, jika kita ingin menurunkan perkalian tiga fungsi berbeda berikut ini:<\/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-f6710d72c4b3c57f51a1855a274e4faf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x\\cdot e^{2x} \\cdot \\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk menyelesaikan turunan, kita harus menerapkan aturan turunan dari hasil kali tiga fungsi, oleh karena itu: <\/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-5c925055bae8204915ed1a7ce6fea5cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3\\cdot e^{2x} \\cdot \\text{sen}(x)+3x\\cdot 2e^{2x} \\cdot \\text{sen}(x)+3x\\cdot e^{2x} \\cdot \\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"454\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-de-un-producto\"><\/span> Demonstrasi rumus turunan suatu produk<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Terakhir, kami akan mendemonstrasikan rumus turunan perkalian. Anda tidak harus menghafalnya, tetapi ada baiknya untuk selalu memahami dari mana rumusnya berasal. \ud83d\ude42<\/p>\n<p> Dari definisi matematis turunan:<\/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-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Misalkan fungsi <em>z<\/em> merupakan hasil kali dua fungsi yang berbeda:<\/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-7221f2fe5a3cdb96186c0c3bac490818_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)\\cdot g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Maka turunan dari <em>z<\/em> menurut definisinya 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-2883cdf5f77c221fda1e72fd5f69ad33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{\\bigl[f(x+h)\\cdot g(x+h)\\bigr]-\\bigl[f(x)\\cdot g(x)\\bigr]}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"371\" style=\"vertical-align: -13px;\"><\/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-0245613adf61bb881d95fdd9f88cf16f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x+h)-f(x)\\cdot g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"342\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Seperti yang kita ketahui, jika kita menjumlahkan suatu suku dengan cara penjumlahan dan pengurangan, maka tidak akan mempengaruhi hasilnya selama keduanya merupakan suku yang sama. Oleh karena itu, kita dapat melanjutkan ke langkah berikutnya:<\/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-2dc1543688ce758352ae824c04f44766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x+h)\\color{orange}\\bm{-f(x+h)\\cdot g(x)+f(x+h)\\cdot g(x)}\\color{black}-f(x)\\cdot g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"696\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Kami sekarang menggunakan properti batas untuk memisahkan batas sebelumnya menjadi dua batas berbeda:<\/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-79db4573036eb08e40df29d50582ab22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x+h)-f(x+h)\\cdot g(x)}{h}+\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)-f(x)\\cdot g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"582\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Kami mengekstrak faktor persekutuan dalam pembilang kedua 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-6e21b5ddadb3c3767bd0292a4b25a471_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\bigl(g(x+h)-g(x)\\bigr)}{h}+\\lim_{h \\to 0}\\frac{g(x)\\bigl(f(x+h)-f(x)\\bigr)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"526\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Di sisi lain, kita mengetahui hasil dari limit 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-682c9bad316f22a6e608611a63af1dbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{h \\to 0}f(x+h)=f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"155\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kita dapat menyederhanakan batasannya:<\/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-9df631d571432bd2bbe55b94bb6cb608_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}f(x+h)\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}+\\lim_{h \\to 0}g(x)\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"563\" style=\"vertical-align: -13px;\"><\/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-77c3c708c8dcd5ee55fb3dfc24900eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f(x)\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}+g(x)\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"468\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Terakhir, dengan melihat dua limit yang tersisa, masing-masing sesuai dengan definisi turunan suatu fungsi. Oleh karena itu, kesetaraan dapat disederhanakan:<\/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-6d25565e3730d9f761ed2f01b1522946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f(x)\\cdot g'(x)+g(x)\\cdot f'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"252\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Atau setara:<\/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-b1e429dfae9a3659f78a3851759c6320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan hasil kali dua fungsi (rumus). Selain itu, Anda juga dapat melihat beberapa contoh turunan perkalian fungsi dan bahkan berlatih menyelesaikan soal turunan perkalian. Rumus turunan suatu produk Turunan suatu hasil kali dua fungsi yang berbeda sama dengan hasil kali turunan fungsi pertama dengan fungsi kedua yang tidak terdiferensiasi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\"> <span class=\"screen-reader-text\">Turunan dari suatu produk (atau perkalian)<\/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-35","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 suatu produk (rumus dan latihan yang diselesaikan)<\/title>\n<meta name=\"description\" content=\"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.\" \/>\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-hasil-perkalian\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Turunan suatu produk (rumus dan latihan yang diselesaikan)\" \/>\n<meta property=\"og:description\" content=\"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:01:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derive-dun-produit.webp\" \/>\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=\"3 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-hasil-perkalian\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari suatu produk (atau perkalian)\",\"datePublished\":\"2023-09-17T11:01:09+00:00\",\"dateModified\":\"2023-09-17T11:01:09+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\"},\"wordCount\":590,\"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-hasil-perkalian\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\",\"name\":\"\u25b7 Turunan suatu produk (rumus dan latihan yang diselesaikan)\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-09-17T11:01:09+00:00\",\"dateModified\":\"2023-09-17T11:01:09+00:00\",\"description\":\"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Turunan dari suatu produk (atau perkalian)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Turunan suatu produk (rumus dan latihan yang diselesaikan)","description":"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/","og_locale":"id_ID","og_type":"article","og_title":"\u25b7 Turunan suatu produk (rumus dan latihan yang diselesaikan)","og_description":"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.","og_url":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/","article_published_time":"2023-09-17T11:01:09+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derive-dun-produit.webp"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"3 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Turunan dari suatu produk (atau perkalian)","datePublished":"2023-09-17T11:01:09+00:00","dateModified":"2023-09-17T11:01:09+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/"},"wordCount":590,"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-hasil-perkalian\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/","url":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/","name":"\u25b7 Turunan suatu produk (rumus dan latihan yang diselesaikan)","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-09-17T11:01:09+00:00","dateModified":"2023-09-17T11:01:09+00:00","description":"Kami menjelaskan cara menurunkan hasil kali atau perkalian fungsi (rumus). Dengan latihan yang diselesaikan pada turunan produk fungsi.","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/turunan-dari-hasil-perkalian\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Turunan dari suatu produk (atau perkalian)"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/id\/#website","url":"https:\/\/mathority.org\/id\/","name":"Mathority","description":"Di mana rasa ingin tahu bertemu dengan perhitungan!","publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/mathority.org\/id\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/id\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38","name":"Tim Mathority","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Tim Mathority"},"sameAs":["http:\/\/mathority.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/35\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=35"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=35"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}