{"id":195,"date":"2023-08-18T23:44:51","date_gmt":"2023-08-18T23:44:51","guid":{"rendered":"https:\/\/rumusmatematika.id\/?p=195"},"modified":"2023-11-17T05:44:22","modified_gmt":"2023-11-17T05:44:22","slug":"rumus-turunan-fungsi","status":"publish","type":"post","link":"https:\/\/tuturpedia.com\/rumusmatematika\/rumus-turunan-fungsi\/","title":{"rendered":"Rumus Turunan Fungsi Dalam Matematika"},"content":{"rendered":"<h2><a href=\"https:\/\/rumusmatematika.id\/rumus-turunan-fungsi\/\" target=\"_blank\" rel=\"noopener\"><b>Rumus<\/b><\/a><strong>\u00a0Turunan Fungsi dalam Matematika: Konsep, Penerapan, dan Contoh Soal<\/strong><\/h2>\n<p>Turunan adalah salah satu konsep utama dalam kalkulus yang memungkinkan kita untuk memahami perubahan suatu fungsi terhadap variabelnya. Dalam matematika, turunan digunakan untuk mengukur laju perubahan, gradien, dan titik infleksi dalam suatu fungsi. Dalam artikel ini, kita akan membahas secara mendalam konsep turunan, rumus turunan, dan memberikan contoh soal untuk memperjelas penerapannya.<\/p>\n<figure id=\"attachment_385\" aria-describedby=\"caption-attachment-385\" style=\"width: 1000px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"rumus turunan fungsi wp-image-385 size-full\" title=\"rumus turunan fungsi\" src=\"https:\/\/rumusmatematika.id\/wp-content\/uploads\/2023\/08\/Rumus-Turunan-Fungsi.jpg\" alt=\"rumus turunan fungsi\" width=\"1000\" height=\"563\" srcset=\"https:\/\/tuturpedia.com\/rumusmatematika\/wp-content\/uploads\/2023\/08\/Rumus-Turunan-Fungsi.jpg 1000w, https:\/\/tuturpedia.com\/rumusmatematika\/wp-content\/uploads\/2023\/08\/Rumus-Turunan-Fungsi-768x432.jpg 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><figcaption id=\"caption-attachment-385\" class=\"wp-caption-text\">rumus turunan fungsi<\/figcaption><\/figure>\n<h3><strong>Konsep Dasar Turunan:<\/strong><\/h3>\n<p><strong>Definisi Turunan:<\/strong> Dalam matematika, turunan (<span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\u2032(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> atau <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">df<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) dari suatu fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> adalah fungsi lain yang menyatakan laju perubahan nilai <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> terhadap perubahan variabel <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Notasi Turunan:<\/strong><\/p>\n<ul>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">df<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: Notasi Leibniz.<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\u2032(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>: Notasi Newton.<\/li>\n<li><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">lim\u2061\u210e\u21920\ufffd(\ufffd+\u210e)\u2212\ufffd(\ufffd)\u210e<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">lim<span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mrel mtight\">\u2192<\/span>0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">f<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">f<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: Definisi limit dari turunan.<\/li>\n<\/ul>\n<p><strong>Rumus Turunan Fungsi Dasar:<\/strong><\/p>\n<ol>\n<li><strong>Turunan Konstan:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(\ufffd)=0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> (Di mana <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> adalah konstanta).<\/li>\n<li><strong>Turunan <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(\ufffd)=1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><strong>Turunan <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(\ufffd\ufffd)=\ufffd\ufffd\ufffd\u22121<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (Di mana <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> adalah bilangan bulat).<\/li>\n<li><strong>Turunan <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(sin\u2061(\ufffd))=cos\u2061(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">))<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><strong>Turunan <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(cos\u2061(\ufffd))=\u2212sin\u2061(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">))<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><strong>Turunan <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">tan\u2061(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">tan<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>:<\/strong> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(tan\u2061(\ufffd))=sec\u20612(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mop\">tan<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">))<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">sec<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<h3><strong>Rumus Turunan Fungsi Komposit:<\/strong><\/h3>\n<p><strong>Aturan Rantai (Chain Rule):<\/strong> Jika <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd=\ufffd(\ufffd(\ufffd))<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span>, maka turunannya adalah: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd\ufffd=\ufffd\ufffd\ufffd\ufffd\u22c5\ufffd\ufffd\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">df<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">df<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>Aturan Produk (Product Rule):<\/strong> Jika <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd=\ufffd\u22c5\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><\/span><\/span><\/span><\/span>, maka turunannya adalah: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd\ufffd=\ufffd\u2032\ufffd+\ufffd\ufffd\u2032<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">v<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mord\"><span class=\"mord mathnormal\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>Aturan Quotient (Quotient Rule):<\/strong> Jika <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd=\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, maka turunannya adalah: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd\ufffd=\ufffd\u2032\ufffd\u2212\ufffd\ufffd\u2032\ufffd2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">\u2032<\/span><\/span><\/span><span class=\"mord mathnormal mtight\">v<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3><strong>Langkah-langkah Menggunakan <a href=\"https:\/\/akupintar.id\/info-pintar\/-\/blogs\/turunan-fungsi-aljabar-pengertian-rumus-aplikasi-contoh-soal\" target=\"_blank\" rel=\"noopener\">Rumus Turunan:<\/a><\/strong><\/h3>\n<ol>\n<li><strong>Identifikasi Fungsi (<span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>):<\/strong> Tentukan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> yang akan diturunkan.<\/li>\n<li><strong>Terapkan Rumus Turunan:<\/strong> Gunakan rumus turunan yang sesuai dengan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>. Ini melibatkan penggunaan aturan turunan dasar atau aturan rantai, produk, atau quotient jika fungsi tersebut merupakan fungsi komposit atau hasil perkalian atau pembagian fungsi.<\/li>\n<li><strong>Sederhanakan Ekspresi:<\/strong> Sederhanakan hasil turunan sebisa mungkin untuk mendapatkan bentuk yang lebih terbaca dan dapat diinterpretasikan.<\/li>\n<li><strong>Simpulkan Hasil:<\/strong> Sajikan hasil turunan sebagai fungsi turunan dari fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>.<\/li>\n<\/ol>\n<h3><strong>Contoh Soal dan Penyelesaian:<\/strong><\/h3>\n<p><strong>Contoh Soal 1:<\/strong> Hitung turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)=3\ufffd2+2\ufffd+1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Penyelesaian:<\/strong><\/p>\n<ol>\n<li>Identifikasi fungsi: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)=3\ufffd2+2\ufffd+1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>.<\/li>\n<li>Terapkan rumus turunan: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(3\ufffd2+2\ufffd+1)=6\ufffd+2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>Sederhanakan ekspresi: Hasilnya sudah sederhana.<\/li>\n<li>Simpulkan hasil: Turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> adalah <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">6\ufffd+2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>.<\/li>\n<\/ol>\n<p><strong>Contoh Soal 2:<\/strong> Hitung turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)=sin\u2061(2\ufffd)\u22c5\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Penyelesaian:<\/strong><\/p>\n<ol>\n<li>Identifikasi fungsi: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)=sin\u2061(2\ufffd)\u22c5\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/li>\n<li>Terapkan rumus turunan dengan aturan produk: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(sin\u2061(2\ufffd)\u22c5\ufffd\ufffd)=cos\u2061(2\ufffd)\u22c5\ufffd\ufffd+sin\u2061(2\ufffd)\u22c5\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>Sederhanakan ekspresi: Hasilnya sudah sederhana.<\/li>\n<li>Simpulkan hasil: Turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> adalah <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061(2\ufffd)\u22c5\ufffd\ufffd+sin\u2061(2\ufffd)\u22c5\ufffd\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/li>\n<\/ol>\n<p><strong>Contoh Soal 3:<\/strong> Hitung turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u210e(\ufffd)=tan\u2061(\ufffd)\ufffd2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">t<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Penyelesaian:<\/strong><\/p>\n<ol>\n<li>Identifikasi fungsi: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u210e(\ufffd)=tan\u2061(\ufffd)\ufffd2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">t<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/li>\n<li>Terapkan rumus turunan dengan aturan quotient: <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd\ufffd(tan\u2061(\ufffd)\ufffd2)=sec\u20612(\ufffd)\u22c5\ufffd2\u22122\ufffd\u22c5tan\u2061(\ufffd)\ufffd4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">t<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">s<\/span><span class=\"mtight\">e<\/span><span class=\"mtight\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span>2<span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mop mtight\"><span class=\"mtight\">t<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>Sederhanakan ekspresi: Sederhanakan dengan menggabungkan suku-terkuat dan faktor.<\/li>\n<li>Simpulkan hasil: Turunan fungsi <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u210e(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> adalah <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">sec\u20612(\ufffd)\u22c5\ufffd2\u22122\ufffd\u22c5tan\u2061(\ufffd)\ufffd4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">s<\/span><span class=\"mtight\">e<\/span><span class=\"mtight\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span>2<span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mop mtight\"><span class=\"mtight\">t<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/li>\n<\/ol>\n<h3><strong>Penerapan Rumus Turunan dalam Kehidupan Sehari-hari:<\/strong><\/h3>\n<ol>\n<li><strong>Ilmu Fisika:<\/strong> Dalam fisika, turunan digunakan untuk mengukur kecepatan, percepatan, dan perubahan lainnya dalam variabel-variabel fisika.<\/li>\n<li><strong>Ekonomi:<\/strong> Dalam ekonomi, turunan dapat digunakan untuk mengukur laju pertumbuhan ekonomi atau perubahan variabel ekonomi lainnya.<\/li>\n<li><strong>Ilmu Komputer:<\/strong> Dalam ilmu komputer, turunan digunakan dalam algoritma-algoritma optimisasi, machine learning, dan grafika komputer.<\/li>\n<li><strong>Biologi:<\/strong> Dalam biologi, turunan dapat digunakan untuk mengukur laju pertumbuhan populasi, reaksi kimia dalam sel, dan proses biologis lainnya.<\/li>\n<li><strong>Analisis Data:<\/strong> Dalam analisis data, turunan digunakan untuk menentukan titik kritis, titik infleksi, dan pola perubahan dalam data.<\/li>\n<\/ol>\n<h3><strong>Kesimpulan:<\/strong><\/h3>\n<p>Rumus turunan fungsi adalah alat matematika yang sangat kuat dan diterapkan secara luas dalam berbagai bidang. Dengan memahami konsep dasar turunan, aturan turunan, dan langkah-langkah untuk menghitung turunan suatu fungsi, kita dapat menggali wawasan mendalam tentang perilaku fungsi dan memahami perubahan dalam suatu sistem. Penerapan rumus turunan melibatkan banyak disiplin ilmu, dan pemahaman yang baik tentang konsep ini mempersiapkan seseorang untuk mengatasi tantangan matematika dan aplikasinya dalam ilmu pengetahuan dan kehidupan sehari-hari.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rumus\u00a0Turunan Fungsi dalam Matematika: Konsep, Penerapan, dan Contoh Soal Turunan adalah salah satu konsep utama dalam kalkulus yang memungkinkan kita&nbsp;[&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":385,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[508,514,500,507,501,503,515,516,517,518,512,499,510,505,504,506,509,511,513,502],"class_list":["post-195","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-rumus-matematika","tag-contoh-soal-turunan-fungsi-aljabar","tag-fungsi-turunan","tag-integral","tag-integral-adalah","tag-rumus-integral","tag-rumus-turunan","tag-rumus-turunan-fungsi-aljabar","tag-rumus-turunan-pertama","tag-rumus-turunan-trigonometri","tag-soal-turunan","tag-soal-turunan-fungsi-aljabar","tag-turunan","tag-turunan-cos","tag-turunan-fungsi","tag-turunan-fungsi-aljabar","tag-turunan-fungsi-trigonometri","tag-turunan-pertama","tag-turunan-sin","tag-turunan-sin-cos-tan","tag-turunan-trigonometri"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/195","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/comments?post=195"}],"version-history":[{"count":5,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/195\/revisions"}],"predecessor-version":[{"id":667,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/195\/revisions\/667"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media\/385"}],"wp:attachment":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media?parent=195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/categories?post=195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/tags?post=195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}