{"id":29,"date":"2023-09-17T11:03:23","date_gmt":"2023-09-17T11:03:23","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-sinus\/"},"modified":"2023-09-17T11:03:23","modified_gmt":"2023-09-17T11:03:23","slug":"turunan-sinus","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-sinus\/","title":{"rendered":"Berasal dari payudara"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan cara membuat turunan sinus (rumus). Anda akan menemukan contoh turunan fungsi sinusoidal dan menyelesaikan latihan langkah demi langkah untuk berlatih. Selain itu, kami juga menunjukkan kepada Anda turunan kedua sinus, turunan kebalikan dari sinus, dan kami bahkan menunjukkan rumus turunan sinus. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-seno\"><\/span> Apa turunan dari sinus?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan dari fungsi sinus adalah fungsi kosinus. Oleh karena itu, turunan sinus x sama dengan kosinus x.<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fdc142e7ff766dcf7fcd24b16e11ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"375\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jika terdapat suatu fungsi dalam argumen sinus, maka turunan sinus adalah kosinus fungsi tersebut dikalikan dengan turunan fungsi tersebut.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus turunan sinus yang kedua ini diperoleh dengan menerapkan aturan rantai pada rumus pertama. Jadi, secara ringkas rumus turunan fungsi sinus adalah: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-du-sinus.webp\" alt=\"berasal dari payudara\" class=\"wp-image-1872\" width=\"392\" height=\"282\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-seno\"><\/span> Contoh turunan sinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui apa itu rumus turunan sinus, kami akan menjelaskan beberapa contoh turunan trigonometri jenis ini agar Anda memahami sepenuhnya cara menurunkan fungsi sinus. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-seno-de-2x\"><\/span> Contoh 1: Turunan dari sinus 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8eb4985d571a4ead05f1f6289197249f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam argumen sinus kita mempunyai fungsi yang berbeda dengan x, jadi kita perlu menggunakan rumus berikut untuk mendapatkan sinusnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Turunan dari 2x adalah 2, jadi turunan sinus dari 2x adalah hasil kali cosinus 2x dikali 2. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3fdd6b2afbc2c387f9160474119139f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(2x)\\cdot 2=2\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"503\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-seno-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari sinus x kuadrat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-856ab4d35ee160a6b966a748ec9cf4f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus turunan fungsi sinus adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan karena turunan x <sup>2<\/sup> sama dengan 2x, maka turunan sinus x yang dipangkatkan 2 adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-901d9c0780a330a0d10d9f6d0185bbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"423\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-seno-al-cubo\"><\/span> Contoh 3: Turunan dari sinus pangkat tiga<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6428f8178ef3b768b1ec0a673f31c814_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^3(x^5+4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"162\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam contoh ini, fungsi sinus terdiri dari fungsi lain, oleh karena itu kita harus menggunakan aturan berikut untuk membedakan sinus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, turunan dari fungsi tersebut adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ec8461861a7213d371d7dc6cff1cc92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3\\text{sen}^2(x^5+4x)\\cdot \\text{cos}(x^5+4x)\\cdot (5x^4+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"368\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <u style=\"text-decoration-color:#ff951b;\">Untuk menurunkan fungsi ini, Anda juga harus menerapkan<\/u> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-potensial-daya\/\">rumus turunan suatu pangkat<\/a><\/span> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"segunda-derivada-del-seno\"><\/span>Turunan kedua dari sinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya kita akan menganalisis turunan kedua dari fungsi sinus, karena sebagai fungsi trigonometri mempunyai ciri-ciri tertentu.<\/p>\n<p> Seperti yang kita lihat di atas, turunan dari sinus adalah kosinus. Nah, turunan dari cosinus adalah sinus tetapi sudah berubah tanda. Artinya <strong>turunan kedua dari sinus tersebut adalah sinus itu sendiri tetapi telah berubah tanda<\/strong> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a312c69d71be2df495ba30f6e3b85e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{sen}(x)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=\\text{cos}(x)\\\\[2ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{sen}(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"157\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Namun, jika argumen sinusnya bukan x, kondisi ini berubah karena kita perlu menyeret suku aturan rantai: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a6a3a1255d5494e320a50ef02bce9d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{sen}(u)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=\\text{cos}(u)\\cdot u' \\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{sen}(u)\\cdot u'^2 +\\text{cos}(u)\\cdot u'' \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-del-seno-inverso\"><\/span>Turunan sinusoidal terbalik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Seperti yang telah diketahui, setiap fungsi trigonometri mempunyai fungsi invers, sehingga invers sinus juga terdiferensiasi.<\/p>\n<p> <strong>Turunan invers sinus<\/strong> sama dengan hasil bagi turunan fungsi argumen dibagi akar kuadrat satu dikurangi kuadrat fungsi argumen.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8fbeb5e099f046c572b9076a3e65b80b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^{-1}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"412\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa sinus invers juga disebut arcsinus.<\/p>\n<p> Misalnya, turunan sinus terbalik dari 5x adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6946743939fbacc11ac050625151ea97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^{-1}(5x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{5}{\\sqrt{1-(5x)^2}}=\\cfrac{5}{\\sqrt{1-25x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"553\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-seno\"><\/span> Latihan soal turunan sinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hitung turunan fungsi sinusoidal berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91a8a2e764daa0e57ffd835005c8c474_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sen}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e80e9e86c1ff2373d4321dbf0b348d8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{sen}(x^2+5x-9)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acda934e5f1e150c3657c7c179dae04e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }\\displaystyle f(x)=\\text{sen}\\left(\\frac{x}{4}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"144\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5dd5bfe722128418bd89665bb3d7fc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sen}^4(5x^3-10x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25cef83962dcc595ea141212c144424c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sen}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1761cfbdc805de80c6edab26613014cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=2\\text{sen}(x^4-3x^3)-7\\text{sen}^2(x^5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0c6093fe6364e806ee4adb980e6ae1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=7\\text{cos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c4f15d01ad3f2dae29e0e6e4944b050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\text{cos}(x^2+5x-9)\\cdot (2x+5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ec1bb477b6f8b9d62adffa38288667b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }\\displaystyle f'(x)=\\text{cos}\\left(\\frac{x}{4}\\right)\\cdot \\frac{1}{4}=\\frac{\\text{cos}\\left(\\frac{x}{4}\\right)}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"256\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d54d16bf947c61429cb47f9613701cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=4\\text{sen}^3(5x^3-10x^2)\\cdot \\text{cos}(5x^3-10x^2)\\cdot (15x^2-20x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"473\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a5b66e0c4e67d903aea56caef9e72df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f'(x)=\\text{cos}\\bigl(\\ln(x)\\bigr)\\cdot \\cfrac{1}{x} =\\cfrac{\\text{cos}\\bigl(\\ln(x)\\bigr)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5002d567a4412d1a78c369ff26ebb66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f'(x)=2\\text{cos}(x^4-3x^3)\\cdot (4x^3-9x^2)-14\\text{sen}(x^5)\\cdot \\text{cos}(x^5)\\cdot 5x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"504\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-del-seno\"><\/span> Demonstrasi turunan sinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pada bagian ini kita akan menunjukkan bahwa turunan dari sinus x adalah cosinus dari x dengan menggunakan definisi turunannya, yaitu:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Dalam hal ini fungsi yang akan diturunkan adalah sin(x), maka:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9af97a03363cd676667ad58135760ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{sen}(x+h)-\\text{sen}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"247\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Sinus suatu penjumlahan dapat ditulis ulang dengan menerapkan identitas trigonometri berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0836929c5c4ae666d530ad9946e1a191_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}(a+b)=\\text{sen}(a)\\text{cos}(b)+\\text{cos}(a)\\text{sen}(b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dbebd45e9fdfaa9e6ade3b6a4bfad716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{sen}(x)\\text{cos}(h)+\\text{cos}(x)\\text{sen}(h)-\\text{sen}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"381\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Kita ubah pecahan tersebut menjadi dua pecahan yang penyebutnya sama. Operasi ini dapat kita lakukan berkat hukum limit suatu jumlah.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3368ab9ecc3a19ad382f85707d6e66cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\left[\\frac{\\text{sen}(x)(\\text{cos}(h)-1)}{h}+\\frac{\\text{cos}(x)\\text{sen}(h)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"375\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-819a10da8fb503b9797c855f0a6208bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\text{sen}(x)\\frac{\\text{cos}(h)-1}{h}+\\lim_{h \\to 0}\\text{cos}(x)\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"377\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/sifat-hukum-batas\/\">hukum batasan<\/a><\/span><\/p>\n<p> Suku sinus dari x dan cosinus dari x tidak bergantung pada nilai h, oleh karena itu kita dapat mengeluarkannya dari limit:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ae7a3b5022abcb1941be4a0b6a02287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{sen}(x)\\cdot\\lim_{h \\to 0}\\frac{\\text{cos}(h)-1}{h}+\\text{cos}(x)\\cdot\\lim_{h \\to 0}\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"402\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Yang harus kita lakukan sekarang adalah menerapkan dua limit trigonometri berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14300dcf4010d732b8568b9b4460b5e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\text{sen}(x)}{x}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-51835176b411ca1ec4f37835a83685fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{1-\\text{cos}(x)}{x}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"146\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Catatan:<\/strong> Demonstrasi dua limit trigonometri sebelumnya dapat Anda cari di mesin pencari website kami.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cfbe7d4af77ff230e9e7a059414e90e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{sen}(x)\\cdot 0+\\text{cos}(x)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-863dc523f1b112a07352b60c8dfdc2b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"109\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Maka kita tunjukkan bahwa turunan sinus x adalah kosinus x.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan cara membuat turunan sinus (rumus). Anda akan menemukan contoh turunan fungsi sinusoidal dan menyelesaikan latihan langkah demi langkah untuk berlatih. Selain itu, kami juga menunjukkan kepada Anda turunan kedua sinus, turunan kebalikan dari sinus, dan kami bahkan menunjukkan rumus turunan sinus. Apa turunan dari sinus? Turunan dari fungsi sinus adalah &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-sinus\/\"> <span class=\"screen-reader-text\">Berasal dari payudara<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[38],"tags":[],"class_list":["post-29","post","type-post","status-publish","format-standard","hentry","category-derivatif"],"yoast_head":"<!-- This site is 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