{"id":385,"date":"2023-07-03T15:44:25","date_gmt":"2023-07-03T15:44:25","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/"},"modified":"2023-07-03T15:44:25","modified_gmt":"2023-07-03T15:44:25","slug":"turunan-sinus-hiperbolik","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/","title":{"rendered":"Turunan dari sinus hiperbolik"},"content":{"rendered":"<p>Di sini Anda akan menemukan cara menurunkan sinus hiperbolik (rumus). Selain itu, Anda akan melihat beberapa contoh penyelesaian turunan sinus hiperbolik. Dan terakhir, kita buktikan rumus turunan fungsi trigonometri jenis ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-seno-hiperbolico\"><\/span> Rumus yang berasal dari sinus hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan dari sinus hiperbolik x adalah kosinus hiperbolik dari 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-5824c2bfe983f8a9b725fab69a97ecca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"394\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, <strong>turunan sinus hiperbolik suatu fungsi<\/strong> sama dengan hasil kali kosinus hiperbolik fungsi tersebut dan 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-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebenarnya kedua rumus di atas sama, yang membedakan hanyalah pada rumus kedua kita menerapkan aturan rantai. Dan karena turunan x adalah 1, maka fungsinya tidak berubah. <\/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-hyperbolique.webp\" alt=\"turunan dari sinus hiperbolik\" class=\"wp-image-2021\" width=\"423\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat, rumus turunan sinus hiperbolik sangat mirip dengan <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-sinus\/\">rumus turunan sinus<\/a><\/span> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-seno-hiperbolico\"><\/span> Contoh turunan sinus hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui apa itu rumus turunan sinus hiperbolik, sekarang kita lanjutkan menyelesaikan beberapa contoh turunan sinus hiperbolik. Jadi, tentunya Anda sudah tidak ragu lagi bagaimana cara melakukannya. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-seno-hiperbolico-de-2x\"><\/span> Contoh 1: Turunan dari sinus hiperbolik 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-11e5d630f508c66d1be884d9a6454d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, pada argumen sinus hiperbolik, kita memiliki fungsi yang berbeda dengan x, oleh karena itu, kita harus menggunakan rumus turunan sinus hiperbolik dengan aturan rantai untuk mencari turunannya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Turunan dari 2x adalah 2, jadi turunan sinus hiperbolik dari 2x adalah kosinus hiperbolik dari 2x dikalikan 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-4e763d6973e52217ac14f6f6b3344737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(2x)\\cdot 2=2\\text{cosh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"533\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-seno-hiperbolico-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari sinus hiperbolik 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-432b20159f3f131533249e4ee44702e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus turunan fungsi sinus hiperbolik 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-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebaliknya, turunan fungsi kuadrat x <sup>2<\/sup> adalah 2x. Oleh karena itu, turunan dari seluruh fungsi 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-56db45ee5a51f7ed624f7e88ce4cf906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"443\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-seno-hiperbolico\"><\/span> Bukti rumus turunan sinus hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Terakhir, kami akan mendemonstrasikan rumus turunan sinus hiperbolik. Untuk melakukan ini, kita akan mulai dari definisi matematis sinus hiperbolik:<\/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-ef003e8f8367d5cacacb4d67fb8dbd01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x)=\\cfrac{e^x-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Kami sekarang menyimpulkan dua sisi persamaan:<\/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-39aa6ef096997dc19e3850036a95b0d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{senh}(x)\\bigr)'=\\left(\\frac{e^x-e^{-x}}{2}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"201\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Untuk menurunkan ruas kanan persamaan, kita akan menggunakan rumus turunan pembagian:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c11def15692e1374b5f75743bfc04b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}'(x)=\\frac{(e^x+e^{-x})\\cdot 2}{2^2}=\\frac{e^x+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"284\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-dari-fungsi-eksponensial\/\">turunan fungsi eksponensial dengan basis e<\/a><\/span><\/p>\n<p> Dan tepatnya kita telah sampai pada ungkapan yang mendefinisikan kosinus hiperbolik. Sehingga turunan sinus hiperbolik terbukti :<\/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-fb3756efaf241b9435c36856a5dad2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}'(x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"143\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan cara menurunkan sinus hiperbolik (rumus). Selain itu, Anda akan melihat beberapa contoh penyelesaian turunan sinus hiperbolik. Dan terakhir, kita buktikan rumus turunan fungsi trigonometri jenis ini. Rumus yang berasal dari sinus hiperbolik Turunan dari sinus hiperbolik x adalah kosinus hiperbolik dari x. Oleh karena itu, turunan sinus hiperbolik suatu fungsi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\"> <span class=\"screen-reader-text\">Turunan dari sinus hiperbolik<\/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-385","post","type-post","status-publish","format-standard","hentry","category-derivatif"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Turunan dari sinus hiperbolik - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari sinus hiperbolik - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan cara menurunkan sinus hiperbolik (rumus). Selain itu, Anda akan melihat beberapa contoh penyelesaian turunan sinus hiperbolik. Dan terakhir, kita buktikan rumus turunan fungsi trigonometri jenis ini. Rumus yang berasal dari sinus hiperbolik Turunan dari sinus hiperbolik x adalah kosinus hiperbolik dari x. Oleh karena itu, turunan sinus hiperbolik suatu fungsi &hellip; Turunan dari sinus hiperbolik Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T15:44:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5824c2bfe983f8a9b725fab69a97ecca_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari sinus hiperbolik\",\"datePublished\":\"2023-07-03T15:44:25+00:00\",\"dateModified\":\"2023-07-03T15:44:25+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\"},\"wordCount\":286,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Derivatif\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\",\"name\":\"Turunan dari sinus hiperbolik - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-07-03T15:44:25+00:00\",\"dateModified\":\"2023-07-03T15:44:25+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Turunan dari sinus hiperbolik\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Turunan dari sinus hiperbolik - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/","og_locale":"id_ID","og_type":"article","og_title":"Turunan dari sinus hiperbolik - Mathority","og_description":"Di sini Anda akan menemukan cara menurunkan sinus hiperbolik (rumus). Selain itu, Anda akan melihat beberapa contoh penyelesaian turunan sinus hiperbolik. Dan terakhir, kita buktikan rumus turunan fungsi trigonometri jenis ini. Rumus yang berasal dari sinus hiperbolik Turunan dari sinus hiperbolik x adalah kosinus hiperbolik dari x. 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