{"id":34,"date":"2023-09-17T11:01:40","date_gmt":"2023-09-17T11:01:40","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/"},"modified":"2023-09-17T11:01:40","modified_gmt":"2023-09-17T11:01:40","slug":"turunan-dari-pengurangan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/","title":{"rendered":"Turunan dari pengurangan"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan fungsi (rumus). Anda juga akan menemukan contoh turunan pengurangan dan menyelesaikan latihan langkah demi langkah untuk berlatih. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-resta\"><\/span> Rumus turunan dari suatu pengurangan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan dari pengurangan dua fungsi sama dengan mengurangkan turunan masing-masing fungsi secara terpisah.<\/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-2eb280531ada831cf451f6440ac3cb7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)-g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)-g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dengan kata lain, membedakan dua fungsi secara terpisah lalu mengurangkannya sama dengan mengurangkan fungsi terlebih dahulu lalu mengambil turunannya. <\/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-d-une-soustraction-1.webp\" alt=\"turunan dari pengurangan\" class=\"wp-image-2053\" width=\"243\" height=\"243\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Demikian pula, aturan diferensiasi yang sama berlaku untuk pengurangan dua fungsi atau lebih, jadi jika kita melakukan pengurangan tiga, empat, lima,\u2026 fungsi, kita perlu membedakan masing-masing fungsi secara terpisah lalu mengurangkannya.<\/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-8bc282473a7f7560eebc97db66bb8f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)- g(x)- h(x)- \\dots\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex]z'(x)=f'(x)-g'(x)- h'(x)- \\dots\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Seperti yang Anda lihat, rumus turunan selisih fungsi sangat mirip dengan aturan turunan suatu penjumlahan.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-suatu-jumlah\/\">turunan dari sejumlah fungsi<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-una-resta\"><\/span> Contoh turunan dari pengurangan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui rumus turunan dari suatu pengurangan, sekarang kita beralih ke menganalisis beberapa contoh turunan dari jenis operasi ini untuk memahami sepenuhnya bagaimana pengurangan suatu fungsi diturunkan. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-resta-de-funciones-potenciales\"><\/span> Contoh 1: Turunan dari pengurangan fungsi potensial<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-ea1b9e305c4c2b69fa19c4458715aa03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-4x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Turunan pengurangan dua fungsi sama dengan selisih turunan masing-masing fungsi secara terpisah. Oleh karena itu, pertama-tama kita akan menghitung turunan setiap fungsi secara terpisah: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-57\">\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-d80e76a954f8534d7a4229864ab4c7ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ x^3=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" 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-c96360191da869602a245eff5e086e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 4x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"77\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Oleh karena itu, turunan dari seluruh fungsi 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-e0227a82cee066220095b0cb8a73276f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"120\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-resta-de-funciones-distintas\"><\/span> Contoh 2: Turunan dari pengurangan fungsi yang berbeda<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-3359936db8c2787dcb9d1c9eb1afb194_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x)-\\log_7(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk membedakan fungsi pengurangan, pertama-tama Anda harus membedakan kedua fungsi tersebut secara terpisah, lalu mengurangkannya. <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-60\">\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-88911e0c596da5c7e5cd27ae8411eda1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ \\text{cos}(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"158\" 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-440c15ed64920bf34bb54bc46cece0e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\log_7 (x^2)=\\cfrac{2x}{x^2\\cdot \\ln(7)}=\\cfrac{2}{x\\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"261\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Dan setelah membuat kedua turunannya, kita kurangi dengan orde awal yang sama: <\/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-2e37e34506772fb550148f02cbc9ebdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\text{sen}(x)-\\cfrac{2}{x\\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-resta-al-cuadrado\"><\/span> Contoh 3: Turunan dari pengurangan 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-3fea677e30feb8612d8d9ff7108a1625_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(x^7-2x^3-9\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"178\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita mempunyai fungsi komposit, karena merupakan pengurangan antara tiga fungsi kuadrat. Oleh karena itu kita harus menggunakan rumus turunan suatu fungsi potensial dan aturan rantai untuk menghitung turunan seluruh 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-4592b6df0dc2ed15a07f4382a817372f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2\\left(x^7-2x^3-9\\right)\\cdot \\left(7x^6-6x^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"285\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-potensial-daya\/\">rumus turunan suatu pangkat<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-resta\"><\/span> Latihan soal turunan pengurangan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Turunkan pengurangan 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-554714ddbd627e6e4db47875cf74ced0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=9x^3-5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" 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-a44e7914b191221833e66b56cfb85c0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=4x^5-6x^4-x^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" 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-d2ffe7ee4f97af710c28c149b75ee6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\left(-3x^7-2x^5\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"196\" 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-e2a65669468838e35b6314f216c94c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\ln(5x^2+3x)-\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" 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-b2a845babbdb5c1108fb183266b265cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=8x^3-e^{5x}-\\sqrt{8x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"241\" 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 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-a7619c845d231badc6717536370242c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=27x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" 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-69d4ff912fd82dfe90ff0996b1782195_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=20x^4-24x^3-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" 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-efabd300a93704ba1ef8dd75ab565c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=4\\left(-3x^7-2x^5\\right)^3\\cdot (-21x^6-10x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"345\" 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-ef722845586f56e6fa7aff817614b6b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{10x+3}{5x^2+3x}-\\bilg(-\\text{sen}(x)\\bigr)=\\cfrac{10x+3}{5x^2+3x}+\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"420\" style=\"vertical-align: -14px;\"><\/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-4cdf075f9332987c97d80e87aa96be07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=24x^2-5e^{5x}-\\cfrac{8}{2\\sqrt{8x+2}}=24x^2-5e^{5x}-\\cfrac{4}{\\sqrt{8x+2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"476\" style=\"vertical-align: -16px;\"><\/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-una-resta\"><\/span> Bukti turunan dari suatu pengurangan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya kita akan mendemonstrasikan rumus turunan pengurangan fungsi dari definisi turunan, 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-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> Jadi jika z adalah selisih dua fungsi 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-d195ec32e5caf166e1ae253669f8cea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)-g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" 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-17f0dc216847872551637f676d1ff0b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{z(x+h)-z(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"215\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Kita mengganti z dengan pengurangan fungsi dalam ekspresi limit:<\/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-40e01069bb5a50a9f8706e0b232a6c4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{\\bigl[f(x+h)-g(x+h)\\bigr]-\\bigl[f(x)-g(x)\\bigr]}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"389\" 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-0c008a2b368b6662d4184f781c60b73d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-g(x+h)-f(x)+g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"359\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Sekarang kita akan melakukan transformasi untuk memisahkan pecahan dan memperoleh pengurangan dua 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-e88137498b1755e2cbe6a93a99d2b769_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}+\\frac{-g(x+h)+g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"392\" 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-4d2339c16c7467a19eb2387b7d84985e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}-\\frac{g(x+h)-g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"379\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Dengan menerapkan hukum limit, kita dapat memisahkan persamaan di atas menjadi dua limit yang berbeda. Karena limit suatu pengurangan sama dengan pengurangan limit:<\/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-bd3b4a827d5e04a2c084d0b2cfc0a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}-\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"394\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Jika diperhatikan lebih dekat, setiap limit berhubungan dengan turunan suatu fungsi, yang berarti rumus turunan selisih terpenuhi:<\/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-5e0eb0254f80f131053caa8ee1480b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'(x)-g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan cara menurunkan fungsi (rumus). Anda juga akan menemukan contoh turunan pengurangan dan menyelesaikan latihan langkah demi langkah untuk berlatih. Rumus turunan dari suatu pengurangan Turunan dari pengurangan dua fungsi sama dengan mengurangkan turunan masing-masing fungsi secara terpisah. Dengan kata lain, membedakan dua fungsi secara terpisah lalu mengurangkannya sama dengan mengurangkan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\"> <span class=\"screen-reader-text\">Turunan dari pengurangan<\/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-34","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 dari pengurangan (rumus dan latihan yang diselesaikan)<\/title>\n<meta name=\"description\" content=\"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705\" \/>\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-pengurangan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Turunan dari pengurangan (rumus dan latihan yang diselesaikan)\" \/>\n<meta property=\"og:description\" content=\"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:01:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2eb280531ada831cf451f6440ac3cb7d_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-pengurangan\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari pengurangan\",\"datePublished\":\"2023-09-17T11:01:40+00:00\",\"dateModified\":\"2023-09-17T11:01:40+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\"},\"wordCount\":361,\"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-pengurangan\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\",\"name\":\"\u25b7 Turunan dari pengurangan (rumus dan latihan yang diselesaikan)\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-09-17T11:01:40+00:00\",\"dateModified\":\"2023-09-17T11:01:40+00:00\",\"description\":\"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Turunan dari pengurangan\"}]},{\"@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 dari pengurangan (rumus dan latihan yang diselesaikan)","description":"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705","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-pengurangan\/","og_locale":"id_ID","og_type":"article","og_title":"\u25b7 Turunan dari pengurangan (rumus dan latihan yang diselesaikan)","og_description":"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705","og_url":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/","article_published_time":"2023-09-17T11:01:40+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2eb280531ada831cf451f6440ac3cb7d_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"2 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Turunan dari pengurangan","datePublished":"2023-09-17T11:01:40+00:00","dateModified":"2023-09-17T11:01:40+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/"},"wordCount":361,"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-pengurangan\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/","url":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/","name":"\u25b7 Turunan dari pengurangan (rumus dan latihan yang diselesaikan)","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-09-17T11:01:40+00:00","dateModified":"2023-09-17T11:01:40+00:00","description":"Kami menjelaskan cara menurunkan fungsi pengurangan (rumus). \u2705 Dengan latihan yang diselesaikan langkah demi langkah pada turunan pengurangan. \u2705","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/turunan-dari-pengurangan\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Turunan dari pengurangan"}]},{"@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\/34","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=34"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/34\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=34"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=34"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}