{"id":387,"date":"2023-07-03T13:35:39","date_gmt":"2023-07-03T13:35:39","guid":{"rendered":"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/"},"modified":"2023-07-03T13:35:39","modified_gmt":"2023-07-03T13:35:39","slug":"turunan-dari-garis-singgung-hiperbolik","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/","title":{"rendered":"Turunan dari garis singgung hiperbolik"},"content":{"rendered":"<p>Di sini Anda akan menemukan turunan dari tangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat beberapa contoh penyelesaian turunan garis singgung hiperbolik. Dan terakhir, kami tunjukkan rumus turunan tangen hiperbolik. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-tangente-hiperbolica\"><\/span> Rumus turunan tangen hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Turunan tangen hiperbolik x sama dengan 1 dibagi kuadrat kosinus hiperbolik x.<\/strong> Turunan garis singgung x juga setara dengan kuadrat garis potong hiperbolik x, dan 1 dikurangi kuadrat garis singgung hiperbolik x.<\/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-9a7c392afdb3bbf504e167e15fb2fee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tanh}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{1}{\\text{cosh}^2(x)}=\\text{sech}^2(x)=1-\\text{tanh}^2(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"338\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sebaliknya, jika dalam argumen fungsi kita mempunyai fungsi selain x, kita harus menerapkan aturan rantai. Lalu ketiga rumus turunan tangen hiperbolik 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-b5ee01c6675067b20f71ea8ac4efcfe5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tanh}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{u'}{\\text{cosh}^2(u)}=\\text{sech}^2(u)\\cdot u'=\\left(1-\\text{tanh}^2(u)\\right)\\cdot u'\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"409\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ini tidak berarti bahwa setiap kali kita menurunkan garis singgung hiperbolik kita harus menggunakan ketiga rumus tersebut, namun kita dapat menggunakan salah satu rumus tersebut untuk menurunkannya. Jadi, bergantung pada fungsi argumen tangen hiperbolik, akan lebih baik menggunakan satu rumus atau lainnya. Di bawah ini adalah beberapa contoh di mana Anda dapat melihat bagaimana tangen hiperbolik suatu fungsi diturunkan. <\/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-de-la-tangente-hyperbolique.webp\" alt=\"turunan dari garis singgung hiperbolik\" class=\"wp-image-2072\" width=\"420\" height=\"366\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Turunan garis singgung hiperbolik hampir sama dengan turunan garis singgung, namun memiliki detail kecil yang membuatnya sangat berbeda. Anda bisa melihat perbedaannya pada link berikut:<\/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-garis-singgung\/\">rumus turunan tangen<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-tangente-hiperbolica\"><\/span> Contoh turunan dari garis singgung hiperbolik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah melihat apa rumus turunan tangen hiperbolik, berikut beberapa contoh penyelesaian turunan fungsi trigonometri jenis ini agar Anda paham betul cara menurunkan tangen hiperbolik. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-tangente-hiperbolica-de-2x\"><\/span> Contoh 1: Turunan dari garis singgung 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-79ac7ea68ec9b155da28c4fbcaa0ee15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mendapatkan tangen hiperbolik dalam contoh ini, kita akan menggunakan rumus kosinus hiperbolik, meskipun Anda tentu saja dapat menggunakan mana pun yang Anda suka.<\/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-7db9abcf1f642aef23b75d912cde9280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cosh}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"407\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Kita tahu bahwa turunan dari 2x adalah 2, jadi turunan seluruh fungsinya 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-ece3b50dd3b4705574fda3f7cda6e66a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{\\text{cosh}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"425\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-tangente-hiperbolica-de-x-al-cuadrado\"><\/span> Contoh 2: Turunan dari garis singgung 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-ff96c9470dca3d696a7002d26563a63e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Aturan turunan tangen hiperbolik suatu 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-7db9abcf1f642aef23b75d912cde9280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cosh}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"407\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Di satu sisi, kita membedakan fungsi dari argumen x <sup>2<\/sup> , yang menghasilkan 2x, lalu kita menyelesaikan turunan seluruh fungsi menggunakan rumus: <\/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-6d16a26c06c4b3843facf3f0a980a61d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}(x^2)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{\\text{cosh}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"421\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-tangente-hiperbolica-al-cubo\"><\/span> Contoh 3: Turunan dari garis singgung hiperbolik 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-e766da71a69fd53df69de8305a592844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tanh}^3(7x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, kita harus memperoleh tangen hiperbolik dari suatu fungsi yang, terlebih lagi, dipangkatkan. Jadi kita perlu menggunakan rumus turunan fungsi potensial, aturan turunan tangen hiperbolik, dan 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-8a7e6b023f634820c69181cfa8d0a16b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3\\text{tanh}^2(7x^2)\\cdot \\cfrac{14x}{\\text{cosh}^2(7x^2)}}=\\cfrac{42x\\cdot \\text{tanh}^2(7x^2)}{\\text{cosh}^2(7x^2)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"402\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-la-tangente\"><\/span> Bukti turunan garis singgung<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pada bagian ini, kita akan mendemonstrasikan rumus turunan tangen hiperbolik. Dan untuk itu, kita akan mulai dari identitas trigonometri yang menghubungkan ketiga perbandingan trigonometri 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-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Catatan:<\/strong> Untuk memahami pembuktiannya, Anda perlu mengetahui apa <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-sinus-hiperbolik\/\">turunan dari sinus hiperbolik<\/a><\/span> dan apa <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/turunan-kosinus-hiperbolik\/\">turunan dari kosinus hiperbolik<\/a><\/span> . Oleh karena itu, kami menyarankan Anda mengunjungi halaman tertaut sebelum melanjutkan.<\/p>\n<p> Sekarang, mari kita terapkan rumus turunan hasil bagi: <\/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-0b01359155f318f95df8e21e428d2026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left(\\text{tanh}(x)\\right)'=\\left(\\frac{\\text{senh}(x)}{\\text{cosh}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"193\" style=\"vertical-align: -17px;\"><\/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-f6f85187679a1b95d64d3afdb78efd4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=\\cfrac{\\text{cosh}(x)\\cdot \\text{cosh}(x)-\\text{senh}(x)\\text{senh}(x) }{\\text{cosh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"356\" style=\"vertical-align: -19px;\"><\/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-48dd21086a84d52131322f0aa9086a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=\\cfrac{\\text{cosh}^2(x)-\\text{senh}^2(x)}{\\text{cosh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"243\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Kami mengurangi ekspresi pembilang pecahan menggunakan rumus 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-4317a445a90e4d139b47db7cf4a49a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)-\\text{senh}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" 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-d7acd0e926ab13e13a82d0bbed6f20fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=\\cfrac{1}{\\text{cosh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"155\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Seperti yang Anda lihat, persamaan sebelumnya sesuai dengan rumus pertama untuk turunan tangen hiperbolik. Begitu pula dengan garis potong hiperbolik merupakan kebalikan perkalian dari kosinus hiperbolik, sehingga rumus kedua juga diturunkan:<\/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-efd858fd9bbcc28bbba771ddfe60479d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=\\text{sech}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Terakhir, kita dapat sampai pada aturan ketiga turunan tangen hiperbolik dengan mengubah pecahan dari langkah sebelumnya menjadi pengurangan pecahan: <\/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-258c135ebd5bf9f28981900d19ca20e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cosh}^2(x)-\\text{senh}^2(x)}{\\text{cosh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"234\" style=\"vertical-align: -19px;\"><\/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-c8316a3ad4867e7135dfae9a7f49506e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=\\cfrac{\\text{cosh}^2(x)}{\\text{cosh}^2(x)}-\\cfrac{\\text{senh}^2(x)}{\\text{cosh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"245\" style=\"vertical-align: -19px;\"><\/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-acc11824e13677fc21ae1f0e9dd24733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}'(x)=1-\\text{tanh}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"184\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan turunan dari tangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat beberapa contoh penyelesaian turunan garis singgung hiperbolik. Dan terakhir, kami tunjukkan rumus turunan tangen hiperbolik. Rumus turunan tangen hiperbolik Turunan tangen hiperbolik x sama dengan 1 dibagi kuadrat kosinus hiperbolik x. Turunan garis singgung x juga setara dengan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\"> <span class=\"screen-reader-text\">Turunan dari garis singgung 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-387","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 garis singgung 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-dari-garis-singgung-hiperbolik\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Turunan dari garis singgung hiperbolik - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan turunan dari tangen hiperbolik suatu fungsi. Selain itu, Anda akan dapat melihat beberapa contoh penyelesaian turunan garis singgung hiperbolik. Dan terakhir, kami tunjukkan rumus turunan tangen hiperbolik. Rumus turunan tangen hiperbolik Turunan tangen hiperbolik x sama dengan 1 dibagi kuadrat kosinus hiperbolik x. Turunan garis singgung x juga setara dengan &hellip; Turunan dari garis singgung hiperbolik Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-03T13:35:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a7c392afdb3bbf504e167e15fb2fee6_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=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Turunan dari garis singgung hiperbolik\",\"datePublished\":\"2023-07-03T13:35:39+00:00\",\"dateModified\":\"2023-07-03T13:35:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\"},\"wordCount\":452,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Derivatif\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\",\"url\":\"https:\/\/mathority.org\/id\/turunan-dari-garis-singgung-hiperbolik\/\",\"name\":\"Turunan dari garis singgung hiperbolik - 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