{"id":308707,"date":"2022-11-27T08:03:03","date_gmt":"2022-11-27T01:03:03","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=308707"},"modified":"2023-02-06T10:25:24","modified_gmt":"2023-02-06T03:25:24","slug":"turunan-fungsi-aljabar","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/","title":{"rendered":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp\" alt=\"\" class=\"wp-image-308710\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, saat mendengar istilah penurunan pangkat, pasti kamu akan berpikir tentang perpindahan jabatan seseorang ke level yang lebih rendah kan? Apa jadinya jika penurunan pangkat terjadi di dunia Matematika? Tenang, di dunia Matematika <em>gak<\/em> ada jabatan-jabatan tertentu, <em>kok<\/em>. Penurunan pangkat di dunia Matematika biasanya terjadi pada fungsi aljabar, sehingga istilahnya dikenal sebagai turunan fungsi aljabar. Lalu, apa yang dimaksud turunan fungsi aljabar dan bagaimana cara menghitung turunan fungsi aljabar? Yuk, simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Pengertian Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Jika diimplementasikan di dalam grafik fungsi, turunan ini merupakan gradien garis singgung terhadap grafik di titik tertentu. Tingkat turunan fungsi tidak terbatas pada satu tingkat saja, tetapi juga bisa dua tingkat, tiga tingkat, dan seterusnya. Konsep turunan setiap tingkatnya juga sama. Hanya saja, fungsi yang diturunkan berbeda-beda karena mengacu pada hasil turunan sebelumnya.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Konsep Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pada dasarnya, turunan fungsi aljabar merupakan bentuk lain dari suatu limit fungsi yang nilainya mendekati nol. Misalnya saja, seseorang berkendara menggunakan motor dengan kecepatan 60 km\/jam. Saat berkendara, apakah orang tersebut bisa mengondisikan untuk tetap berada di kecepatan itu? Tentu tidak, kan? Lalu, apa artinya 60 km\/jam? Kecepatan tersebut merupakan kecepatan rata-rata. Secara matematis, dirumuskan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/b4gCzGxfe5xLp6Nf2urMdO6flIRmos9plp3_3ZNtzWR9Svpfk9Njl0-ocrbYJrRxDp8RyYsV_XOmQ8JiXTHuS-aEjYs3rj3nYH9aHN2nbJ37JN3R9t4EekdAYFHgkBOhZw_y271Du_JUGRZX-omA56PqsMGpE8_We8qSSxZLK7rrlffITmHgXGvMy7izwNZSdu818pqQug\" alt=\"\" width=\"85\" height=\"56\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ingat, posisi orang tersebut (<em>s<\/em>) selalu berubah setiap waktu (<em>t<\/em>). Artinya, posisi bisa dinyatakan sebagai fungsi waktu (<em>s<\/em><sub>2<\/sub> = <em>f<\/em>(<em>t<\/em>)<em> <\/em>). Nah, <em>t<\/em><em><sub>2<\/sub><\/em> merupakan waktu setelah bergerak selama <em>h<\/em> atau <em>t<\/em><em><sub>2<\/sub><\/em> = <em>t<\/em><em><sub>1<\/sub><\/em> + <em>h<\/em>. Jika disubstitusikan ke persamaan kecepatan rata-rata menjadi:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/n8rc5k02Kh0mMth7aKias6hCSVp7BHotMV21_fEO0-Myf4lJWB4hv9Hs9wtDfUGNzi79bvMVXRKOp3zWBsNlytbBNqeMYINYYf858pUt_uejVoGx6DTQP4GFlX5xA9NAejs05CRO3SgFkO2g0ewx9UwtKIywzP1u4twdVc_uEHI6y9r-FtY6ELTLxwpH28qm_WnN1zZIkw\" alt=\"\" width=\"161\" height=\"90\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk nilai <em>h<\/em> yang sangat kecil, <em>h<\/em> bisa dinyatakan mendekati nol (<em>h<\/em> \u2192 0). Apa artinya? Jika nilai <em>h<\/em> mendekati nol, akan berlaku fungsi kecepatan sesaat seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/uE2nq-wQX_isIXkUyzd6_24uOsmskuqNx9i-cOosQqSqr9tHuxoyNLVSmzOLIUbYj1MczKdcy7JmZOcpSEbUXxgWGLDhOpLFVLFF6NnewHop1XMLHSjYFufiCfE8-I6lY5mRVbAexKunGtnwTchyAdkVUhfobpnuDVx9T3LDDE4tRUhJNp4iZTKHswYI_jLk934DrtHrmA\" alt=\"\" width=\"265\" height=\"50\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Persamaan di atas merupakan bentuk laju perubahan jarak terhadap waktu atau turunan fungsi jarak terhadap waktu.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jika diterapkan pada sembarang <em>f<\/em>(<em>x<\/em>), akan berlaku laju perubahan <em>f<\/em>(<em>x<\/em>) terhadap <em>x<\/em> atau turunan pertama <em>f<\/em>(<em>x<\/em>) terhadap <em>x <\/em>(f\u2019(<em>x<\/em>)), sehingga persamaannya menjadi:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/agCJscXH7M0zXyuiz7mByrCn-6B2iPEwp64-cEqjDUaN4sQfE9afXXa_r19xP2ATAnHV6PvyblejIMa7kx_gIA8tsc4LoX6kO8uhaxe2CPPAj6dKNXGZpblrMs8CMlfOVE68fB0CUNUIfU_3elRWOh8H9O5KywLcFfVVsRwATHqtGpyQw6l-kLZ7zadJrr5r5fBXafgovQ\" alt=\"\" width=\"177\" height=\"40\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Rumus Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Persamaan turunan yang memuat fungsi limit efektif digunakan untuk persamaan fungsi linear atau pangkat 1. Namun, rumus tersebut kurang efektif jika digunakan pada persamaan fungsi aljabar yang derajat polinomnya lebih dari 1 (pangkat lebih dari 1). Untuk itu, kamu bisa menggunakan rumus-rumus berikut.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><em>f<\/em>(<em>x<\/em>) = <em>b<\/em> \u2192 f\u2019(<em>x<\/em>) = 0<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu konstanta akan bernilai nol jika diturunkan, contoh f(x) = 15 \u2192 f\u2019(x) = 0.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><em>f<\/em>(<em>x<\/em>) = <em>bx<\/em> \u2192 f\u2019(<em>x<\/em>) = <em>b<\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Jika variabel <em>x<\/em> diturunkan terhadap <em>x<\/em>, akan menghasilkan 1. Contoh:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>f(<em>x<\/em>) = <em>x<\/em> \u2192 f\u2019(<em>x<\/em>) = 1<\/li>\n\n\n\n<li>f(<em>x<\/em>) = 2<em>x<\/em> \u2192 f\u2019(<em>x<\/em>) = 2<\/li>\n\n\n\n<li>f(<em>x<\/em>) = 5<em>x<\/em> \u2013 3 \u2192f\u2019(<em>x<\/em>) = 5<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><em>f<\/em>(<em>x<\/em>) = <em>ax<\/em><em><sup>n<\/sup><\/em><sup> <\/sup>\u2192 f\u2019(<em>x<\/em>) = <em>nax<\/em><em><sup>n-1<\/sup><\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Rumus di atas berlaku untuk turunan fungsi pangkat, ya. Saat menurunkan suatu fungsi, artinya kamu sedang mencari turunan pangkat dari fungsi tersebut atau pangkatnya menjadi lebih kecil. Misal, jika variabel <em>x<\/em><sup>2<\/sup> diturunkan terhadap <em>x<\/em>, maka derajat variabelnya akan berkurang 1 menjadi <em>x<\/em>. Jika variabel <em>x<\/em><sup>3<\/sup> diturunkan terhadap <em>x<\/em>, maka derajat variabelnya akan berkurang 1 menjadi <em>x<\/em><em><sup>2<\/sup><\/em> dan seterusnya. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f(<em>x<\/em>) = 6<em>x<\/em><sup>4<\/sup> + 2<em>x<\/em><em><sup>3<\/sup><\/em> \u2192 f\u2019(<em>x<\/em>) = (4)(6)<em>x<\/em><sup>3<\/sup> + (3)(2)<em>x<\/em><sup>2<\/sup>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 24<em>x<\/em><sup>3<\/sup> + 6<em>x<\/em><sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Turunan fungsi aljabar juga bisa dinyatakan dalam bentuk notasi Leibniz seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/RkuwJ81SQBdOuOZy2bPcSeSg-OfNZuuXy5-BceNnri8IbwcKFN9EeoM3RVU9ufgM1CFnKe0ArrMTrbBndIJcbcDDvmZGB7ns3zw7wbo9sod818nXwTVGVpDYdv5FfF44DUSuRRWe86C4PllWgXkX0pNZ1TEi8RaErkpZWN9z_xd2sP8z6_4A8VEhzqTcU0q-0c7uw2zoYQ\" alt=\"\" width=\"190\" height=\"103\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bagaimana Quipperian, mudah bukan turunan fungsi aljabar itu?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Sifat-Sifat Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Turunan fungsi aljabar memiliki sifat-sifat tertentu yang nantinya bisa memudahkanmu dalam menyelesaikan soal-soal. Berikut ini sifat-sifat turunan fungsi aljabar.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/ztzsn817h3U_rxzZW2WqveGWXUr2TSYePs4wwRqQzraJI8RA-5X3Ue6h5LrhV7nx9IawpfJWm6NyWL7djBk7NHma7eBKMfXThyXRsH-6I33abdr9T6mqbWKoI5_GZNtJZJauyRsJsR4W9YDa1Oo8HbZb2Tf-wZWCugyt0mTQ8TlizQF0Tn2IU9Vp3Fjc7JIqj6BKX-k3Hw\" width=\"289\" height=\"27\"><sub><\/sub><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat di atas berlaku pada penjumlahan atau pengurangan dua fungsi atau lebih. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/_lV2e7-mVJVMFvekaes8-G_mD1T9DwyOx7bWLZSeXHVgrmOXgW3lQGPxtkYFze7YF6eDLJjMw4kRewjpMqWV6xWyKsxpdBapL93XnmU0b3VrXHstMotP7OGoZaEaeMSVvInsF91itI-2PtkMs4bHEDrW9Ql8JwuL0nBlvj0CWbaRz4CiRGe0JYXVCuQXHE3tBv_2ZH3L_Q\" alt=\"\" width=\"176\" height=\"47\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/OoPnC7vOET5xAduHv0s7yIU3nYt43xKPiaP0EmkppYQfcUxm2eE6XbdxfG3EyVZ62EGYg2DxHINmZKdQaogC_tGLw0voM_zv8OhItI8kKlDOj06mdCDPaK03ooc63tIFAijsoLiVgmEBWzi2Prg7_Bg8QGc7JoYcQrsjo5eKYOh4RG3BU83N3ZN03rsZQRWYEIRcufcTfw\" width=\"358\" height=\"27\"><sub><\/sub><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat di atas berlaku untuk turunan hasil kali fungsi, contohnya pada perkalian antara fungsi <em>u<\/em>(<em>x<\/em>) dan <em>v<\/em>(<em>x<\/em>). Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/53R1e5SLhTJz5DMY8rqdzKjOUq7o3_EYLAXrfYZrQs76Nyk2TvRa-DnGKLxwsTTyjILQlfG5bZYZp0h4GuNASKtzY-k86BqvVD_KDqZ_scrukjMREcfZfLQtjFFhJyRAm4FjeHIfAqhbLpNF72heMDxmkB7eUrq3BpYBmbKBJjeeS_S9KSMgx1Opa7VZhCfrv78geLGYEw\" alt=\"\" width=\"194\" height=\"102\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/w81yAdliR3hrTlIsH-xS3-PG0XWkBk7Q5Gj3VYnXEy9kJrf7oAjqD5NGDHtDSkhH54K_6-pPTBbrubPJl5H9eqLBisujDj0vCotnQji5zRP9tPt3SwoQmYsL4Xou_Mhp3dhL_ONBn5vmR0h-gVQ_zHVbphAUt3rM0H0e7ARwosLYwbKHR_kKopPunuE8Ob2dA7ntqjFe2A\" width=\"325\" height=\"54\"><sub><\/sub><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat di atas berlaku untuk turunan fungsi pembagian, contoh pembagian antara fungsi <em>u<\/em>(<em>x<\/em>) dan <em>v<\/em>(<em>x<\/em>). Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/OioFKlcGs8vfNvG6J7CYYHHoEMmB2TJfqwpCaLmxPZAdI8VIDJo3cCqDZ9mrZtwMVK0sS5zaCvAqOwG4tGXaEm8bTusW_hLhvKt8QTKU72lz34J6suH07U0zqSDv2VATR3MlvOGqQpeR1rnkCHm_i26IsiyXIfQ1hFgDYhK5rn5k2o73OSMVuIAbRYUhTOKpQGLHyvemhA\" alt=\"\" width=\"221\" height=\"234\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/dpszJLrO56bqAVr8IqJI7RAHa3_kJAfKIfbi3-FByPN25tVtVmxkM0a0d7ElvtktvlxswdWYtKxd07UNZxZ1Pkgp6lXafxWS1u4whrAJmdzxZVcXgf3TTaDSmf7KA44YMiRxzYy89ewQgzyAVrB_2QtGx6ypZcPLOO_FMhRO_TXp-uLMo-UkwNUcJPe-YWHsLfzotz_EPQ\" width=\"324\" height=\"49\"><sub><\/sub><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/w90GvpMhqf4QXCeBO7E3BNZm3xtO2TwlI7yDLW1y-jaPW5FwTMVM3skksX_q0e2JnEEeqVMgWSLErrc-0-h0ADfwNjdyaXFuNKn1YuxzQAKLAL4ed5v4YX0urHqaRfjH3uSV_DhH4KXXWGuIF2yUelVrjECe1J0R87kes6ecOX8khIuwXmPGiDifKBYktPR3j6PuPqkGKg\" alt=\"\" width=\"159\" height=\"129\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/L2PEzBpYJd88UIdTVrEDTYFROGryYrz6X2NqrjE-urbykj2Ky9IkTmdC64u5prfkpP5oQDFsDAS-crPHYVzwKS4X8h2iOPpmiDdc4Rk2y3BlIqaSeQYehYEika-oZDGEaCoxW1wS-22VSsrl6W6myqCCj9fIADNSSJ2Nc1gyNkZGcWMzJ0gvD7MQxCrh_k74w920f0cTPg\" width=\"383\" height=\"64\"><sub><\/sub><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Sifat di atas merupakan aturan rantai turunan fungsi aljabar. Selain menurunkan fungsi yang dipangkatkan, kamu juga harus menurunkan keseluruhan fungsinya.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Adapun contoh turunan fungsi aljabar adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan turunan fungsi aljabar akar berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/OryiTE-VYb7q3b8ucEspAppZK4Yft4LB1lc_XQkKW9nWMOcileJdY3kxtMn4wTuq-ODPEo9rbBTFx5KECSvM99UgvNftyUYIzWiY-5dzdCGwjLcGoOM32WW5sBdM687-g77cSbjiWEcHEgBc2H3xOyQUHT9Txytghz3n6Fy-Tu9SaVzV7y5WI06ELxDQJtYz34_TaL5MqA\" alt=\"\" width=\"122\" height=\"31\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pada soal di atas, berlaku aturan rantai turunan fungsi aljabar. Apa maksud aturan rantai turunan?<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/RxuURcyz0jI4oMFeaWz9Ano5Z6KONjZaoF2I1gv9F81PiZST-0Wi9nwdjb7thN3PmTd29CtjSSiz7xb20vYPqgBeaZ5TuZlj9klfM3yXi3J70gdtSlYABgtm4ezm_wRVmoojAXb2Ry4qzh3wtEzNNsOa0j0lH3qhZOXSfDuiO_EZvP3wuPFJSKQRsDejuUUGcAN66O2ayQ\" alt=\"\" width=\"134\" height=\"62\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus memisalkan 2<em>x<\/em><sup>3<\/sup> \u2013 4<em>x<\/em> sebagai <em>u<\/em>(<em>x<\/em>). Dengan demikian, persamaannya menjadi:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/tgzc2w96gHii3-qwOJoo0gCjRa1I63SZJaT6eOh0yKN-0uORWyQkvDwEUzow6-mCB4NvN4BFuYaidCcZcrtiT4exjZ8z_uTwMi6rN6IFd9zgFciRerDZ7AqGl5YdF-XaOE4jV1j15a6W9FsefojX6dirTWtdgbgz08k1K7rQPa1gLHmDcz-wZTG33E7rqtCLxiM59DK5XQ\" alt=\"\" width=\"112\" height=\"38\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan hasil turunannya menggunakan sifat nomor 5.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/YpXRjPhHYprjmsEFhRnWD-tQewLs8olFefN7sxM-7GoIt3dNDA-ehPC7vzhp_HLnHocPCdkEeYXmvrMgha82-bYCFWV5Pxnk1_w4eCtqYEvniCoLKNEjroDMQIpfEIjPBtrtp2exFOUvcZGoJ1zEoq2rx1-cDnUBQoTSh062mbFD0A-Mm9VCvgXCFtqwBEcfgsCGJsqWqA\" alt=\"\" width=\"136\" height=\"59\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah mencari turunan <em>u<\/em>, kamu harus mencari turunan <em>f<\/em>(<em>x<\/em>).<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/gU0khgP2yUze1D5-9mEHq5VMlb_IDI1mE6RN9qJCJq7SDSA6otK23eEA5eGYpFbyEtUusJipk8WH5zD38mVGK9mOGV3hRQiVz1WR24PsB6YWhnT7JuFAujVx8GI2Cx-PL4Z2nUFhAfFIVzF3NveSdPr-T8tMXReH0apeJ2wE8WVFhv17pAtmg5H-7Pcl8bzilHw_UTRKew\" alt=\"\" width=\"183\" height=\"167\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Aplikasi Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Turunan fungsi aljabar biasa diaplikasikan pada beberapa masalah matematis seperti gradien garis singgung kurva seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/Z-qZUhgUFY0rf-VqngmP3RB7BGVZHsM6Ki2ADHq9A-e3S7OgpT6bp1MI7qcCr2cAOhtjIXl6IMz5opw_sVg1e2uXDOeT8iVefp1Egk_1fkuIpweGQEjQ_mHuxrlF9I8zQfwGkMx7oZwUPAA0bq37PfSZMMH5RDduPJErEUIUG_Q-KBqX3yWv1ZcIzs-WFMteZBtzD2kyHg\" alt=\"\" width=\"443\" height=\"256\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari grafik di atas, kamu akan mendapati garis sekan dan garis normal. Garis sekan adalah garis yang memotong grafik di dua titik. Persamaan gradien garis singgungnya bisa dinyatakan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/FpipUOvF6BpwCW5NDOxDDPsqW3Ueg-GrpmE-mqd9jwolau688qN_4G6x50LOYVfPW6idMxSwjNxE-_-2-y8_0TlzsbcNJmydQtNmCCHBC6YoMzro6aulrnRUEr-v7cL97WmeqDgaVzh4x_aUNwFD7f99pKCPqpJ0ng6d-BjrWrIEuGDz3m9F_itGMZFfEcIMqJPUxRlnGQ\" alt=\"\" width=\"106\" height=\"58\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari gambar di atas, <em>x<\/em><sub>2<\/sub> = <em>x<\/em><sub>1<\/sub> + <em>h<\/em>, dengan <em>y<\/em> = <em>f<\/em>(<em>x<\/em>), sehingga diperoleh:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/ElFEZyoSSSysA_w3HSu_viI3cWkw7GyxcSWCmGEkKttsacdKtSQ8ka-eMoxrszYJGIa1oTsKrHSENs6gzQO_f4Y3F0dX2tc9K5ifYfydBmGu4qT6QOefVLwCAJZjubYfhf7FBGTz3UJT7ZFCw0Pg5MvxI69zxToMxzMvttzRXjvcuUtHxVj0lvwbLG-sO-FKeGhl457pPw\" alt=\"\" width=\"169\" height=\"212\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Saat A mendekati B, nilai <em>h<\/em> akan semakin kecil. Jika nilai <em>h<\/em> sudah mendekati nol, artinya garis <em>k <\/em>akan menjadi garis singgung <em>l<\/em> dengan gradien <em>m<\/em><sub>1<\/sub> di titik A (<em>x<\/em><sub>1<\/sub>, <em>y<\/em><sub>1<\/sub>). Oleh sebab itu, diperoleh persamaan:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/uYvPArAWn0R4ZPcZsnD2BfkRSVVha5wl5F1WrYuaYIdQNPnSvkYGzt0x55VO5bfi5eEJHoEhRICGqGyGsf3AHS4SSNCBNmrMzjjzKHQW2mVzSlj4fF8Y04MU4d7ymIXAdXYsIIIWS_JVxCvKiskZqA6v-l0-r9rpdefCnaEoFyRcV1ssiHLa2UJ81Ww-jPkdevHpFiz1_w\" alt=\"\" width=\"252\" height=\"79\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, gradien merupakan turunan pertama dari fungsi suatu kurva atau grafik.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/vMo8nFP3EJOfnQxlpWT8VfEYF3iBXODP1mIpc6JSUBaj7iCKyc6oaHybCFQZ67jcbAvK_QuNQGBbTkswwNcxa22FSzbel0zD2lSOcAhaIUtRT0W8p7c4Gh-bzxEliQw5fcD14uoVswzedy3YA5IzQvXB07plBU2eyvaa3-qUSc-WgsXmbOMKEiwa3eflr5lw_h8vfe1BFA\" alt=\"\" width=\"80\" height=\"30\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jika nilai gradien sudah diketahui, kamu bisa menentukan persamaan garis singgungnya dengan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Wam1p_IPqmaLV74HF1nawsL_tWMxAHuMZEafeWucCmqnMLK8yF51phLuU-O9jeKg1PMvCK1j9ypkKoqir5Q9RuxBvnKnIEgJ7jp1aHpR5Gr5CTEs4cs5wXiHmzRuISZn87W8c6WuRxng0KK60082oAX8S7sRTcYHLY_U8YYZbEAQVN5ItVu9Ilnvg-U2ghjA8getkz6h0g\" alt=\"\" width=\"132\" height=\"30\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Soal Turunan Fungsi Aljabar<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mengasah kemampuanmu tentang materi ini, yuk simak contoh soal berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 1<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan persamaan garis yang menyinggung kurva <em>y<\/em> = x<sup>2<\/sup> \u2013 4<em>x<\/em> \u2013 5 di titik absis 1!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus mencari titik ordinat dengan mensubstitusikan <em>x<\/em> = 1 ke persamaan kurvanya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>y<\/em> = x<sup>2<\/sup> \u2013 4<em>x<\/em> \u2013 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(<em>x<\/em>) =&nbsp; x<sup>2<\/sup> \u2013 4<em>x<\/em> \u2013 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(1) = 1<sup>2<\/sup> \u2013 4(1) \u2013 5&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(2) = -8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari perhitungan di atas diperoleh koordinat titik singgungnya, yaitu (1, -8).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan gradien garis singgungnya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/k-fsaw4_LdRnZ5AaFMR0O6n1cDwZvBlJgpC8g1ptMG-SZruBZf4SzYzyiBCG-8k-WJNa9dio7jpB7PD9QhLD5kjFXIrsUXjK7bT7qr8AGRox1PAp5iuz6Zi84q-Opgjmd9jJB_pLf965jnvFFtL9oIaw9p8DXkqHhLSfyDMuQ8WjbsA0dcrUv_rMwDW3vieRE0DTFrlalw\" alt=\"\" width=\"120\" height=\"81\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, persamaan garisnya bisa dinyatakan sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>y<\/em> \u2013 <em>y<\/em><sub>1<\/sub> = <em>m<\/em> (<em>x<\/em> \u2013 <em>x<\/em><sub>1<\/sub>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2194 <em>y<\/em> \u2013 (-8) = -2(<em>x<\/em> \u2013 1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2194 <em>y<\/em> = -2<em>x<\/em> \u2013 6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, persamaan garis yang menyinggung kurva <em>y<\/em> = x<sup>2<\/sup> \u2013 4<em>x<\/em> \u2013 5 di titik absis 1 adalah <em>y<\/em> = -2<em>x<\/em> \u2013 6.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah bola ditendang dengan sudut elevasi tertentu hingga mengalami gerak parabola. Persamaan gerak bola tersebut dinyatakan sebagai <em>h<\/em>(<em>t<\/em>) = 4<em>t<\/em> \u2013 2<em>t<\/em><sup>2<\/sup>. Berapakah ketinggian maksimum bola tersebut?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Besaran yang dicari pada soal adalah ketinggian maksimum. Artinya, kecepatan di titik tertinggi sama dengan nol. Sementara itu, persamaan yang tertera pada soal adalah persamaan lintasan. Dengan demikian, kamu harus menentukan turunan pertama persamaan lintasannya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Fzs602-71btkZIa5960fCNaU7roc_24re32e3gp6ZSGJoQLgIBSVaZlt2ea-THnWgB9Kax5AIhJzGsTVLUKnYJ6wd1SmSy1F85NVy1lqS_yMqJlTZEY8hLWLkZkP_1CSMjvSGIQUXKlDtfZzPidCntCvTdFcHIKCvX_4RyuaViFeGhOdyojYiD6U31p9rFHcM5EAICzx_A\" alt=\"\" width=\"224\" height=\"129\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, substitusikan nilai <em>t<\/em> = 1 s ke persamaan lintasannya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>h<\/em>(<em>t<\/em>) = 4<em>t<\/em> \u2013 2<em>t<\/em><sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>h<\/em>(1) = 4(1) \u2013 2(1)<sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>h<\/em>(1) = 2 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, ketinggian maksimum bola tersebut adalah 2 m.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh soal 3<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu unit UMKM pengolahan makanan ringan mampu memproduksi <em>x<\/em> unit makanan dengan biaya (2<em>x<\/em><sup>2<\/sup> \u2013 4<em>x<\/em> + 10) dalam ribuan rupiah untuk setiap unit. Jika makanan ringan akan habis dengan harga jual Rp10.000 setiap unit, berapakah keuntungan maksimum per unit yang diperoleh UMKM tersebut?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Banyak makanan = <em>x<\/em> unit<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Biaya produksi per unit = 2<em>x<\/em><sup>2<\/sup> \u2013 4<em>x<\/em> + 10 dalam ribuan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Harga jual per unit = 10 (ribuan)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, misalkan keuntungan perusahaan sebagai <em>g<\/em>(<em>x<\/em>).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>g<\/em>(<em>x<\/em>) = untung = harga jual \u2013 biaya produksi, sehingga:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>g<\/em>(<em>x<\/em>) = 10<em>x<\/em> \u2013 (2<em>x<\/em><sup>2<\/sup> \u2013 4<em>x<\/em> + 10)<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 10<em>x<\/em> \u2013 2<em>x<\/em><sup>3<\/sup> + 4<em>x<\/em><sup>2<\/sup> &#8211; 10<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= \u2013 2<em>x<\/em><sup>3<\/sup> + 4<em>x<\/em><sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keuntungan maksimum diperoleh jika g\u2019(<em>x<\/em>) = 0. Dengan demikian:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(<em>x<\/em>) = \u2013 2<em>x<\/em><sup>3<\/sup> + 4<em>x<\/em><sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g\u2019(<em>x<\/em>) = -6<em>x<\/em><sup>2<\/sup> + 8<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">0 = -6<em>x<\/em><sup>2<\/sup> + 8<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">-6<em>x<\/em><sup>2<\/sup> + 8<em>x<\/em> = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3<em>x<\/em><sup>2<\/sup> &#8211; 4<em>x <\/em>= 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em>(3<em>x<\/em> \u2013 4) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> = 0 atau <em>x<\/em> = 4\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">nilai <em>x<\/em> yang memenuhi = 4\/3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, substitusikan nilai <em>x<\/em> = 4\/3 ke persamaan <em>g<\/em>(<em>x<\/em>).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g(4\/3) = \u2013 2(4\/3)<sup>3<\/sup> + 4(4\/3)<sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= -4,74 + 7,11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 2,37<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, keuntungan maksimum yang diperoleh UMKM tersebut adalah Rp2.370 per unit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk melihat materi lengkapnya, yuk buruan gabung <a href=\"https:\/\/www.quipper.com\/id\/video\/\">Quipper Video<\/a>. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, saat mendengar istilah penurunan pangkat, pasti kamu akan berpikir tentang perpindahan jabatan seseorang ke level yang lebih rendah kan? Apa jadinya jika&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":308710,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[679384825],"ppma_author":[679386823,679386836],"class_list":["post-308707","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-11"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog\" \/>\n<meta property=\"og:description\" content=\"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya\" \/>\n<meta property=\"og:url\" content=\"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/\" \/>\n<meta property=\"og:site_name\" content=\"Quipper Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/QuipperVideoID\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-11-27T01:03:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-06T03:25:24+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"853\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"Wilman Juniardi, Pamela Natasa, S.Pd.\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:site\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Wilman Juniardi\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/\"},\"author\":{\"name\":\"Wilman Juniardi\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/35cf1cd343f3f32e71dd12a58241fc4e\"},\"headline\":\"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!\",\"datePublished\":\"2022-11-27T01:03:03+00:00\",\"dateModified\":\"2023-02-06T03:25:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/\"},\"wordCount\":1228,\"publisher\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2022\\\/11\\\/pexels-louis-bauer-249360-1.webp\",\"keywords\":[\"Materi Matematika Kelas 11\"],\"articleSection\":[\"Matematika\"],\"inLanguage\":\"id\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/\",\"name\":\"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2022\\\/11\\\/pexels-louis-bauer-249360-1.webp\",\"datePublished\":\"2022-11-27T01:03:03+00:00\",\"dateModified\":\"2023-02-06T03:25:24+00:00\",\"description\":\"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#primaryimage\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2022\\\/11\\\/pexels-louis-bauer-249360-1.webp\",\"contentUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2022\\\/11\\\/pexels-louis-bauer-249360-1.webp\",\"width\":1280,\"height\":853,\"caption\":\"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/turunan-fungsi-aljabar\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Mapel\",\"item\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/category\\\/mapel\\\/amp\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matematika\",\"item\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/category\\\/mapel\\\/matematika\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#website\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/\",\"name\":\"Quipper Blog\",\"description\":\"Blog Pendidikan - Referensi untuk Siswa &amp; Guru\",\"publisher\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#organization\",\"name\":\"Quipper Indonesia\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/quipper-main-logo.png\",\"contentUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2021\\\/08\\\/quipper-main-logo.png\",\"width\":146,\"height\":40,\"caption\":\"Quipper Indonesia\"},\"image\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/QuipperVideoID\\\/\",\"https:\\\/\\\/x.com\\\/quipper_id\",\"https:\\\/\\\/instagram.com\\\/quipper_id\\\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/35cf1cd343f3f32e71dd12a58241fc4e\",\"name\":\"Wilman Juniardi\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g47d3f59ef50f58e7db6da1f73bb514ec\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g\",\"caption\":\"Wilman Juniardi\"},\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/author\\\/wilmanjuniardi\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog","description":"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya","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:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/","og_locale":"id_ID","og_type":"article","og_title":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog","og_description":"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya","og_url":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/","og_site_name":"Quipper Blog","article_publisher":"https:\/\/www.facebook.com\/QuipperVideoID\/","article_published_time":"2022-11-27T01:03:03+00:00","article_modified_time":"2023-02-06T03:25:24+00:00","og_image":[{"width":1280,"height":853,"url":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","type":"image\/webp"}],"author":"Wilman Juniardi, Pamela Natasa, S.Pd.","twitter_card":"summary_large_image","twitter_creator":"@quipper_id","twitter_site":"@quipper_id","twitter_misc":{"Ditulis oleh":"Wilman Juniardi","Estimasi waktu membaca":"6 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#article","isPartOf":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/"},"author":{"name":"Wilman Juniardi","@id":"https:\/\/quipperhome.wpcomstaging.com\/#\/schema\/person\/35cf1cd343f3f32e71dd12a58241fc4e"},"headline":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!","datePublished":"2022-11-27T01:03:03+00:00","dateModified":"2023-02-06T03:25:24+00:00","mainEntityOfPage":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/"},"wordCount":1228,"publisher":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/#organization"},"image":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#primaryimage"},"thumbnailUrl":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","keywords":["Materi Matematika Kelas 11"],"articleSection":["Matematika"],"inLanguage":"id"},{"@type":"WebPage","@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/","url":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/","name":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya! - Quipper Blog","isPartOf":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#primaryimage"},"image":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#primaryimage"},"thumbnailUrl":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","datePublished":"2022-11-27T01:03:03+00:00","dateModified":"2023-02-06T03:25:24+00:00","description":"Turunan fungsi aljabar adalah fungsi baru hasil penurunan pangkat dari fungsi sebelumnya menurut aturan yang telah ditetapkan. Selengkapnya","breadcrumb":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/"]}]},{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#primaryimage","url":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","contentUrl":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","width":1280,"height":853,"caption":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!"},{"@type":"BreadcrumbList","@id":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/turunan-fungsi-aljabar\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/quipperhome.wpcomstaging.com\/"},{"@type":"ListItem","position":2,"name":"Mapel","item":"https:\/\/quipperhome.wpcomstaging.com\/category\/mapel\/amp\/"},{"@type":"ListItem","position":3,"name":"Matematika","item":"https:\/\/quipperhome.wpcomstaging.com\/category\/mapel\/matematika\/"},{"@type":"ListItem","position":4,"name":"Turunan Fungsi Aljabar: Pengertian, Rumus dan Sifat-sifatnya!"}]},{"@type":"WebSite","@id":"https:\/\/quipperhome.wpcomstaging.com\/#website","url":"https:\/\/quipperhome.wpcomstaging.com\/","name":"Quipper Blog","description":"Blog Pendidikan - Referensi untuk Siswa &amp; Guru","publisher":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/quipperhome.wpcomstaging.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/quipperhome.wpcomstaging.com\/#organization","name":"Quipper Indonesia","url":"https:\/\/quipperhome.wpcomstaging.com\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/quipperhome.wpcomstaging.com\/#\/schema\/logo\/image\/","url":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/08\/quipper-main-logo.png","contentUrl":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2021\/08\/quipper-main-logo.png","width":146,"height":40,"caption":"Quipper Indonesia"},"image":{"@id":"https:\/\/quipperhome.wpcomstaging.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/QuipperVideoID\/","https:\/\/x.com\/quipper_id","https:\/\/instagram.com\/quipper_id\/"]},{"@type":"Person","@id":"https:\/\/quipperhome.wpcomstaging.com\/#\/schema\/person\/35cf1cd343f3f32e71dd12a58241fc4e","name":"Wilman Juniardi","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/secure.gravatar.com\/avatar\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g47d3f59ef50f58e7db6da1f73bb514ec","url":"https:\/\/secure.gravatar.com\/avatar\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g","caption":"Wilman Juniardi"},"url":"https:\/\/quipperhome.wpcomstaging.com\/author\/wilmanjuniardi\/"}]}},"jetpack_featured_media_url":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-louis-bauer-249360-1.webp","jetpack_shortlink":"https:\/\/wp.me\/paV35H-1ij9","jetpack_sharing_enabled":true,"authors":[{"term_id":679386823,"user_id":156447303,"is_guest":0,"slug":"wilmanjuniardi","display_name":"Wilman Juniardi","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/cd17fca70a31023a257817d2bebd64c15c1dd8adbc2f7530803c6dd7ea9148c2?s=96&d=identicon&r=g","0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""},{"term_id":679386836,"user_id":0,"is_guest":1,"slug":"pamela-natasa","display_name":"Pamela Natasa, S.Pd.","avatar_url":{"url":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Pamela-Natasa.webp","url2x":"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Pamela-Natasa.webp"},"0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""}],"_links":{"self":[{"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/posts\/308707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/users\/156447303"}],"replies":[{"embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/comments?post=308707"}],"version-history":[{"count":4,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/posts\/308707\/revisions"}],"predecessor-version":[{"id":312141,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/posts\/308707\/revisions\/312141"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/media\/308710"}],"wp:attachment":[{"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/media?parent=308707"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/categories?post=308707"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/tags?post=308707"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/quipperhome.wpcomstaging.com\/wp-json\/wp\/v2\/ppma_author?post=308707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}