{"id":437,"date":"2023-07-03T04:31:43","date_gmt":"2023-07-03T04:31:43","guid":{"rendered":"https:\/\/mathority.org\/nl\/arccosecante-afgeleide\/"},"modified":"2023-07-03T04:31:43","modified_gmt":"2023-07-03T04:31:43","slug":"arccosecante-afgeleide","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/arccosecante-afgeleide\/","title":{"rendered":"Afgeleide van de cosecante boog"},"content":{"rendered":"<p>Op deze pagina zie je wat de formule is voor de afgeleide van de arccosecant. Daarnaast kun je opgeloste oefeningen zien voor afgeleiden van de boog-cosecans van een functie. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-arcocosecante\"><\/span> Arccosecant-afgeleide formule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de boogcosecans van x is negatief \u00e9\u00e9n over het product van x maal de wortel van x kwadraat minus 1.<\/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-f0d7defc746af3a5f6f4f0c6b9032eb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{x\\cdot \\sqrt{x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Daarom is de <strong>afgeleide van de boogcosecans van een functie<\/strong> gelijk aan minus het quoti\u00ebnt van de afgeleide van die functie gedeeld door de functie maal de wortel van die functie in het kwadraat min \u00e9\u00e9n.<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> In feite zijn de voorgaande twee formules hetzelfde, maar in de tweede uitdrukking wordt de kettingregel toegepast. Als je de identiteitsfunctie x in de u vervangt, krijg je in feite de afgeleide van de boogcosecans van x, aangezien de afgeleide van x \u00e9\u00e9n is. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-derivee-de-larc-cosecant.webp\" alt=\"arccosecans afgeleide formule\" class=\"wp-image-2734\" width=\"463\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Zoals u wel weet, is de boogcosecans de inverse trigonometrische functie van de cosecans, maar de afgeleiden ervan zijn heel verschillend. U kunt de formule voor dit andere type trigonometrische functie bekijken in de volgende link:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/is-afgeleid-van-de-cosecans\/\">afgeleide van de cosecans<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocosecante\"><\/span> Voorbeelden van afgeleide van de cosecante boog<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Als we kijken wat de arccosecante afgeleide regel is, zullen we vervolgens twee voorbeelden van dit type afgeleide oplossen. Maar als u nog vragen heeft over het afleiden van de cosecansboog, kunt u ons deze in de opmerkingen stellen.<\/p>\n<h3 class=\"wp-block-heading\" id=\"block-46cfc7df-b680-41c2-ad53-bd8a19834b32\"> voorbeeld 1<\/h3>\n<p> In dit voorbeeld zullen we zien hoeveel de afgeleide is van de boogcosecans van de kwadratische functie x <sup>2<\/sup> .<\/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-fca6065258c2a26d98bf6b5fb0eb4b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-2a112ce1-0dbe-43d5-95b3-4d8506c1a246\"> Om de afgeleide van de boogcosecans van x kwadraat te berekenen, passen we de formule toe die we hierboven zagen: <\/p>\n<p class=\"has-text-align-center\" id=\"block-f73c7b5e-fb98-43c1-a3bb-52c9144eee8a\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-a4fe1876-f662-49c1-8d09-6a6c4b5528dd\"> De afgeleide van x tot de macht twee is 2x, dus de afgeleide van de samengestelde functie is: <\/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-eb4dcb62cafb03a267428465ac221f2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{x^2\\cdot \\sqrt{\\left(x^2\\right)^2-1}}=-\\cfrac{2x}{x^2\\cdot \\sqrt{x^4-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"582\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" id=\"block-1446420a-0d61-44d3-9e31-8c5935a432a7\"> Voorbeeld 2<\/h3>\n<p> In dit tweede voorbeeld zullen we de boogcosecant van een potenti\u00eble functie afleiden.<\/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-8ef686c080851299fb2bf1960a042424_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(2x^3+9x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-0514a2ea-d85a-4b25-a7db-9c27533e7436\"> We moeten de afgeleide regel van de boogsecant gebruiken om de afgeleide van de gehele functie te vinden.<\/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-319f0b4d00e6c138ce50d898a9948363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{u\\cdot \\sqrt{u^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"469\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-6abf3c5a-c400-48c6-8375-c05fcb255b20\"> Dus in de teller schrijven we de afgeleide van het argument van de functie, en in de noemer herschrijven we de potenti\u00eble functie en vermenigvuldigen we deze met de vierkantswortel van de functie van het argument in het kwadraat min 1:<\/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-ead8a1afc8e88458fea7abdab11ee836_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccosec}(2x^3+9x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{6x^2+9}{(2x^3+9x)\\cdot \\sqrt{\\left(2x^3+9x\\right)^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"582\" style=\"vertical-align: -30px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina zie je wat de formule is voor de afgeleide van de arccosecant. Daarnaast kun je opgeloste oefeningen zien voor afgeleiden van de boog-cosecans van een functie. Arccosecant-afgeleide formule De afgeleide van de boogcosecans van x is negatief \u00e9\u00e9n over het product van x maal de wortel van x kwadraat minus 1. Daarom &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/arccosecante-afgeleide\/\"> <span class=\"screen-reader-text\">Afgeleide van de cosecante boog<\/span> Lees meer &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-437","post","type-post","status-publish","format-standard","hentry","category-derivaten"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Afgeleide van de cosecante boog - 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\/nl\/arccosecante-afgeleide\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Afgeleide van de cosecante boog - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina zie je wat de formule is voor de afgeleide van de arccosecant. 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Daarnaast kun je opgeloste oefeningen zien voor afgeleiden van de boog-cosecans van een functie. Arccosecant-afgeleide formule De afgeleide van de boogcosecans van x is negatief \u00e9\u00e9n over het product van x maal de wortel van x kwadraat minus 1. 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