{"id":402,"date":"2023-07-03T00:18:18","date_gmt":"2023-07-03T00:18:18","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan\/"},"modified":"2023-07-03T00:18:18","modified_gmt":"2023-07-03T00:18:18","slug":"turunan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan\/","title":{"rendered":"Derivatif"},"content":{"rendered":"<p>Di sini kami menjelaskan cara menurunkan semua jenis fungsi. Anda akan menemukan rumus semua turunan disertai dengan contoh dan latihan turunan langkah demi langkah. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formules-derivees.webp\" alt=\"rumus turunan\" class=\"wp-image-2945\" width=\"226\" height=\"226\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-derivadas\"><\/span> Apa itu produk turunan?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Derivatif<\/strong> adalah aturan matematika yang digunakan untuk mempelajari fungsi. Secara khusus, <strong>turunan suatu fungsi di suatu titik<\/strong> merupakan hasil dari suatu limit dan menunjukkan perilaku fungsi di titik tersebut.<\/p>\n<p> Turunan suatu fungsi dinyatakan dengan tanda prima <em>&#8216;<\/em> , artinya fungsi <em>f'(x)<\/em> merupakan turunan dari fungsi <em>f(x)<\/em> .<\/p>\n<p> Secara geometris, arti turunan suatu fungsi di suatu titik adalah kemiringan garis singgung fungsi di titik tersebut. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-de-la-tangente-ligne.webp\" alt=\"pengertian turunan\" class=\"wp-image-2306\" width=\"392\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <strong>Definisi matematis turunan suatu fungsi<\/strong> adalah sebagai berikut:<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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> Namun, turunan suatu fungsi biasanya tidak dihitung menggunakan rumus di atas, melainkan aturan diferensiasi berlaku bergantung pada jenis fungsinya. Semua rumus derivasi dijelaskan di bawah ini.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-las-derivadas\"><\/span>rumus turunan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah melihat pengertian turunan, kita akan melihat cara pembuatannya, menjelaskan masing-masing jenis turunan beserta contohnya. Tujuan dari postingan kali ini adalah agar anda dapat memahami dengan baik konsep turunan, sehingga jika pada akhirnya anda masih ragu tentang cara menurunkan suatu fungsi, anda dapat bertanya kepada kami di kolom komentar.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante\"><\/span>berasal dari suatu konstanta<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Turunan suatu konstanta<\/strong> selalu nol, berapa pun nilai konstanta tersebut.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c7bd8f1aee171f251c313218820e22f0_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=k \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, untuk mencari turunan suatu fungsi konstanta tidak perlu berhitung apa pun, cukup turunannya nol.<\/p>\n<p> Perhatikan contoh praktis turunan konstanta berikut ini: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-561a1b2c2b0347c0cb38ed7565e46fa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3 \\qquad \\longrightarrow\\qquad f'(x)=0\\\\[3ex]g(x)=-5 \\qquad \\longrightarrow\\qquad g'(x)=0\\\\[3ex]h(x)=291 \\qquad \\longrightarrow\\qquad h'(x)=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"265\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-lineal\"><\/span> Turunan dari fungsi linier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Turunan fungsi linier<\/strong> adalah koefisien suku derajat pertama, yaitu turunan fungsi linier <em>f(x)=Ax+B<\/em> sama dengan <em>A<\/em><\/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-c55a9a25283e37ab61dc79856ee92a11_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=Ax+B\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=A \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lihatlah contoh berikut bagaimana jenis fungsi ini diturunkan: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-53d0d8c8814ef6884b442c3c50cce8a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3x-1\\quad\\longrightarrow\\quad f'(x)=3\\\\[3ex]f(x)=5x\\quad\\longrightarrow\\quad f'(x)=5\\\\[3ex] f(x)=-2x+9\\quad\\longrightarrow\\quad f'(x)=-2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-potencia\"><\/span> berasal dari suatu kekuatan<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Turunan suatu pangkat<\/strong> , atau fungsi potensial, adalah hasil kali eksponen pangkat dikalikan pangkatnya dengan pangkat dikurangi 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-1e7df9c631129b040e262f67f36b41be_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, untuk memperoleh suatu pangkat, cukup kalikan fungsi tersebut dengan eksponen dan kurangi satu satuan dari eksponennya.<\/p>\n<p> Misalnya, turunan pangkat x pangkat tiga 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-0c0dd56d2e4a99c896f5e035d51f80be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=3\\cdot x^{3-1}=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Anda dapat berlatih melakukan latihan (dan yang lebih sulit) dari jenis turunan ini di sini:<\/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\/\">latihan yang diselesaikan untuk turunan suatu pangkat<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-raiz\"><\/span> berasal dari suatu akar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><meta charset=\"utf-8\"> <strong>Turunan dari suatu akar,<\/strong> atau fungsi irasional, sama dengan satu dibagi dengan hasil kali indeks akar dikalikan akar yang sama dengan mengurangkan 1 dari eksponen radicand.<\/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-8b8e85735674a043d4fb2c448038ceb8_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=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebagai contoh, di bawah ini Anda dapat melihat turunan dari akar kuadrat dari x yang diselesaikan:<\/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-5e879d493e8b67755617d2aed1743cde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{2\\sqrt{x^{2-1}}}=\\cfrac{1}{2\\sqrt{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"425\" style=\"vertical-align: -16px;\"><\/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-akar-irasional-radikal\/\">latihan yang diselesaikan untuk turunan suatu akar<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-exponencial\"><\/span> Turunan dari fungsi eksponensial<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Turunan suatu fungsi eksponensial<\/strong> bergantung pada apakah basisnya adalah bilangan <em>e<\/em> atau bilangan lain. Oleh karena itu, ada dua rumus untuk menurunkan fungsi jenis ini dan Anda harus menggunakan rumus yang sesuai dengan basis pangkatnya:<\/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-c21e61c79c41a4f27d53a41495521bdd_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=a^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=a^x\\cdot \\ln(a)\\\\[3ex] f(x)=e^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Di bawah ini Anda dapat melihat dua turunan terselesaikan dari jenis fungsi ini: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-90bd19942de37daaf7af04179eaf5e91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=7^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=7^x\\cdot \\ln(7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71dd62c13ea22caa62fb0e8af338fbdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"312\" style=\"vertical-align: -5px;\"><\/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-eksponensial\/\">soal penyelesaian turunan fungsi eksponensial<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-logaritmica\"><\/span> Turunan dari fungsi logaritma<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Turunan suatu fungsi logaritma<\/strong> bergantung pada basis logaritmanya, karena jika logaritmanya natural maka harus diterapkan rumus untuk mencari turunannya dan jika logaritma mempunyai bilangan lain sebagai basisnya maka harus digunakan aturan lain.<\/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-d384075ba6ad6dcfaf82949d33ad397b_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\ln(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x}\\\\[3ex] f(x)=\\log_a(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(a)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Misalnya turunan logaritma basis tiga dari x adalah:<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e61ac2c2f66f8b05dce8760bdec17d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_3(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"397\" style=\"vertical-align: -17px;\"><\/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-logaritma-logaritma-natural-neperian\/\">latihan yang diselesaikan untuk turunan fungsi logaritma<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivadas-trigonometricas\"><\/span>Turunan trigonometri<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Tiga <strong>turunan trigonometri<\/strong> utama merupakan turunan dari fungsi sinus, fungsi cosinus dan fungsi tangen, yang rumusnya 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-a9e9d0157c2b1eb994571ba96aae4f26_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\text{sen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x)\\\\[2.5ex] f(x)=\\text{cos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x)\\\\[1.1ex]f(x)=\\text{tan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{\\text{cos}^2(x)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Secara logika, ada beberapa jenis fungsi trigonometri, seperti fungsi trigonometri hiperbolik, fungsi trigonometri invers, fungsi trigonometri invers, dan fungsi trigonometri hiperbolik. Namun aturan drifting yang paling banyak digunakan adalah tiga aturan di atas.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"reglas-de-derivacion\"><\/span> aturan rujukan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ketika kita melakukan operasi dengan fungsi, turunannya diselesaikan secara berbeda. Untuk melakukan ini, kita perlu menggunakan <strong>aturan diferensiasi<\/strong> , yang memungkinkan kita menurunkan fungsi penjumlahan, pengurangan, perkalian, dan pembagian.<\/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-ba4f3225344df68c84b4437ecb0c7536_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}z(x)=f(x)\\pm g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\pm g'(x)\\\\[4ex] z(x)=f(x)\\cdot g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\\\[4ex]z(x)=\\cfrac{f(x)}{g(x)} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, untuk menyelesaikan turunan dengan operasi, kita tidak hanya perlu menerapkan aturan turunan saja, tetapi kita juga perlu menggunakan rumus untuk setiap jenis turunannya.<\/p>\n<p> Agar Anda dapat mengetahui cara mencari turunan jenis ini, kita akan menyelesaikan beberapa latihan di bawah ini:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">Turunan dari suatu jumlah:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-efca27bad0818b86e6e42ee15a31ed6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x^2+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a8dcfca37df757df3fd79292ead67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=6x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>Seperti yang Anda lihat, untuk menyelesaikan turunan seluruh fungsi, rumus turunan suatu pangkat diterapkan pada setiap suku dari jumlah tersebut.<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">Berasal dari suatu produk:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8c539c8db8dbf532a639e09af47a583a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{x}\\cdot \\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Turunan suku pertama hasil kali adalah 4 <sup>x<\/sup> ln(4), dan turunan sinusnya adalah kosinus. Jadi turunan dari perkalian adalah: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5829940bb4219334d7e238b40a19794e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=4^{x}\\cdot \\ln (4) \\cdot \\text{sen}(x) +4^{x}\\cdot \\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">Turunan dari suatu hasil bagi:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59b390fee61ab3c2cbb4dc2230386658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Pada pembilang dan penyebut suatu pecahan kita mempunyai polinomial, maka untuk mendapatkan turunannya kita perlu menggunakan rumus turunan hasil bagi, rumus turunan penjumlahan (atau pengurangan) dan rumus turunan dari penjumlahan (atau pengurangan) dan rumus turunan dari suatu pecahan. memiliki kekuatan: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-af3f7cb513883d1fa5dadca23701c19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\\\[2ex]&amp;=\\cfrac{15x^4-24x^2+40x^3-64x-10x^4-40x^3}{25x^4+64-80x^2}\\\\[2ex]&amp;=\\cfrac{5x^4-24x^2-64x}{25x^4-80x^2+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-cadena\"><\/span> Aturan rantai<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><meta charset=\"utf-8\"> <strong>Aturan rantai<\/strong> adalah rumus yang digunakan untuk menurunkan fungsi majemuk. Aturan rantai menyatakan bahwa turunan suatu fungsi komposit <em>f(g(x))<\/em> sama dengan turunan <em>f'(g(x))<\/em> dikalikan dengan turunan <em>g'(x)<\/em> .<\/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-662d8c44c904e83267bbca5f968ca546_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=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Gagasan tentang turunan ini umumnya lebih sulit untuk diasimilasikan, jadi kita akan menyelesaikan latihan langkah demi langkah sebagai contoh:<\/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-c1863b1f92befa398b5c8692d239abf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Secara efektif, ini adalah komposisi fungsi karena kita memiliki fungsi x <sup>3<\/sup> di dalam fungsi sinus, oleh karena itu, kita harus menggunakan aturan rantai untuk mencari turunan dari fungsi komposit tersebut.<\/p>\n<p> Di satu sisi, turunan sinus adalah kosinus, sehingga turunan fungsi luarnya adalah kosinus dengan argumen sinus 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-2046d85a1440fe95dccc4d8bb553e2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"441\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Dan sebaliknya, kita menghitung turunan x <sup>3<\/sup> menggunakan rumus turunan suatu pangkat:<\/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-1d045f948b3519322ae6771bd4497d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jadi, turunan dari fungsi komposit bilangan bulat adalah hasil kali kedua turunannya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab755de02fa9196320c59676d77cd2e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3)\\cdot 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"430\" style=\"vertical-align: -5px;\"><\/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\/rantai-aturan-turunan\/\">menyelesaikan latihan turunan dengan aturan rantai<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivabilidad-de-una-funcion\"><\/span> Diferensiabilitas suatu fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Kontinuitas dan diferensiabilitas suatu fungsi<\/strong> pada suatu titik berhubungan sebagai berikut:<\/p>\n<ul>\n<li> Jika suatu fungsi terdiferensiasi di suatu titik, maka fungsi tersebut kontinu di titik tersebut.<\/li>\n<li> Jika suatu fungsi tidak kontinu di suatu titik, maka fungsi tersebut juga tidak terdiferensiasi di titik tersebut.<\/li>\n<\/ul>\n<p> Namun kebalikan dari teorema ini salah, yaitu hanya karena suatu fungsi kontinu di suatu titik tidak berarti fungsi tersebut selalu terdiferensiasi di titik tersebut.<\/p>\n<p> Anda juga dapat melihat apakah suatu fungsi dapat terdiferensiasi pada suatu titik pada grafiknya:<\/p>\n<ul>\n<li> Jika <strong>titik tersebut mulus,<\/strong> maka fungsinya terdiferensiasi pada titik tersebut.<\/li>\n<li> Jika suatu <strong>titik bersudut,<\/strong> maka fungsinya kontinu tetapi tidak terdiferensiasi pada titik tersebut. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-3\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/exercices-resolus-pour-representer-une-fonction-quadratique-incomplete.webp\" alt=\"\" class=\"wp-image-140\" width=\"250\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <span style=\"color:#1976d2;\"><strong>Titik halus<\/strong><\/span> di x=0:<br \/> fungsi kontinu dan terdiferensiasi pada saat ini. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\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\/comment-representer-graphiquement-une-fonction-avec-valeur-absolue.webp\" alt=\"\" class=\"wp-image-230\" width=\"286\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <span style=\"color:#1976d2;\"><strong>Titik miring<\/strong><\/span> di x=2:<br \/> berfungsi kontinu tetapi tidak terdiferensiasi pada saat ini.<\/p>\n<\/div>\n<\/div>\n<p> Anda juga dapat mengetahui apakah suatu fungsi sepotong-sepotong dapat terdiferensiasi di suatu titik dengan menghitung <strong>turunan lateral<\/strong> di titik tersebut: <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 20px; border-radius:20px;\">\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Jika turunan lateral di suatu titik tidak sama, maka fungsi tersebut tidak terdiferensiasi di titik tersebut:<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97c60c64dc01a7e0a9084313d15b0886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) \\neq f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p> Itu tidak dapat dibedakan dalam<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Jika turunan lateral di suatu titik berimpit, maka fungsi tersebut terdiferensiasi di titik tersebut:<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f9477828318b9e6392465762f831642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) = f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p> Ya itu bisa diturunkan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<p> Sekarang mari kita lihat contoh penghitungan turunan suatu fungsi yang didefinisikan sepotong demi sepotong di suatu titik:<\/p>\n<ul>\n<li> Pelajarilah kontinuitas dan diferensiasi fungsi sepotong-sepotong berikut di titik x=2:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a98eee72521c68fd394eb6209a7d0a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=  \\left\\{ \\begin{array}{lcl} 3x^2-6x &amp; \\text{si} &amp;  x<2 \\\\[2ex] 6\\ln (x-1) &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"249\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Fungsi kedua bagian tersebut kontinu pada intervalnya masing-masing, namun perlu diperiksa apakah fungsi tersebut kontinu pada titik kritis x=2. Untuk melakukan ini, kita menyelesaikan batas lateral fungsi di titik:<\/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-dad5bcb0055431aa87a67068c04d2ce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^-} f(x) = \\lim\\limits_{x\\to 2^-} \\bigl(3x^2-6x\\bigr) = 3\\cdot2^2-6\\cdot2=12-12=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"449\" 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-31e1ba2ea2c5fd9fa86e5cefed0e5535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^+} f(x) = \\lim\\limits_{x\\to 2^+} 6\\ln (x-1) = 6\\ln (2-1)=6 \\ln 1=6 \\cdot 0= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"474\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Batas lateral pada titik kritis memberikan hasil yang sama, sehingga fungsinya kontinu di titik x=2.<\/p>\n<p> Setelah kita mengetahui bahwa fungsi tersebut kontinu di x=2, kita akan mempelajari diferensiasi fungsi tersebut pada titik tersebut. Untuk melakukan ini, kami menghitung <strong>turunan lateral<\/strong> dari fungsi yang ditentukan sedikit demi sedikit:<\/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-3709995609d0f69f382ff651e397c00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)= \\left\\{ \\begin{array}{lcl} 6x-6 &amp; \\text{si} &amp;  x<2 \\\\[2ex] \\cfrac{6}{x-1} &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sekarang kita evaluasi setiap turunan lateral pada titik kritis:<\/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-ca27189960575c1151402d040bfa76f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-)=6\\cdot2-6=12-6 = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" 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-058310a16d7d545ea56e99517845842b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^+)=\\cfrac{6}{2-1} = \\cfrac{6}{1} = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Kedua turunan lateralnya memberikan hasil yang sama, sehingga fungsinya terdiferensiasi di x=2 dan nilai turunannya adalah 6:<\/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-aadf046f27916c46f0a302d6e0c34113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-) = f'(2^+) = 6 \\ \\longrightarrow \\ \\bm{f'(2) = 6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"275\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebaliknya, jika turunan lateral memberikan hasil yang berbeda, berarti fungsi tersebut tidak terdiferensiasi pada x=2. Dengan kata lain, turunannya pada titik ini tidak akan ada.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/diferensiasi-suatu-fungsi\/\">latihan yang diselesaikan untuk diferensiasi suatu fungsi<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di sini kami menjelaskan cara menurunkan semua jenis fungsi. Anda akan menemukan rumus semua turunan disertai dengan contoh dan latihan turunan langkah demi langkah. Apa itu produk turunan? Derivatif adalah aturan matematika yang digunakan untuk mempelajari fungsi. Secara khusus, turunan suatu fungsi di suatu titik merupakan hasil dari suatu limit dan menunjukkan perilaku fungsi di &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan\/\"> <span class=\"screen-reader-text\">Derivatif<\/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-402","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>Derivatif - Mathoritas<\/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\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Derivatif - Mathoritas\" \/>\n<meta property=\"og:description\" content=\"Di sini kami menjelaskan cara menurunkan semua jenis fungsi. 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