{"id":436,"date":"2023-07-03T05:06:38","date_gmt":"2023-07-03T05:06:38","guid":{"rendered":"https:\/\/mathority.org\/nl\/boogsecante-drift\/"},"modified":"2023-07-03T05:06:38","modified_gmt":"2023-07-03T05:06:38","slug":"boogsecante-drift","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/boogsecante-drift\/","title":{"rendered":"Arcsecante afgeleide"},"content":{"rendered":"<p>Op deze pagina ziet u wat de afgeleide is van de boogsecant (formule). Je vindt opgeloste oefeningen voor afgeleiden van de boogsecant van een functie. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-arcosecante\"><\/span> Arcsecant-afgeleide formule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de boogsecans van x is \u00e9\u00e9n over het product van x maal de wortel van x kwadraat min 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-c711ae2ad7e63c11dadabe5b1fa34460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(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=\"439\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Daarom is de <strong>afgeleide van de boogsecans van een functie<\/strong> gelijk aan 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-8101c1f6c91528fc3a8c0a3c35509c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(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=\"439\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Het is duidelijk dat de tweede formule vergelijkbaar is met de eerste formule, het enige verschil tussen de twee is dat de kettingregel wordt toegepast in de tweede formule. <\/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\/derive-darcosecant.webp\" alt=\"afgeleide van boogsecant\" class=\"wp-image-2718\" width=\"411\" height=\"292\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Hoewel het misschien vreemd lijkt omdat het inverse functies zijn, heeft de afgeleide van de boogsecans niets te maken met de afgeleide van de secans. U kunt de formule voor de afgeleide van de secans bekijken door hier te klikken:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/afgeleide-van-de-secans\/\">afgeleide van secans<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcosecante\"><\/span> Voorbeelden van boogsecansderivaat <span class=\"ez-toc-section-end\"><\/span><\/h2>\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 boogsecans van de lineaire functie 7x.<\/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-9191ef645841e7a1f497896df1a8b14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-2a112ce1-0dbe-43d5-95b3-4d8506c1a246\"> Om de afgeleide van de boogsecant te vinden, moet je de overeenkomstige formule toepassen, die als volgt luidt: <\/p>\n<p class=\"has-text-align-center\" id=\"block-f73c7b5e-fb98-43c1-a3bb-52c9144eee8a\"><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-8101c1f6c91528fc3a8c0a3c35509c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(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=\"439\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p id=\"block-a4fe1876-f662-49c1-8d09-6a6c4b5528dd\"> De afgeleide van de 7x-functie is 7, dus de afgeleide van de boogsecant van de 7x-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-095e6d51d8dc9dd49fa9cefb1c115ea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{7}{7x\\cdot \\sqrt{(7x)^2-1}}=\\cfrac{1}{x\\cdot \\sqrt{49x^2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" 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 boogsecans 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-109aa2df6a4b0a2d174e98c663b78dca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(x^4-5x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p id=\"block-0514a2ea-d85a-4b25-a7db-9c27533e7436\"> Omdat er een andere term dan x in het argument van de boogsecansfunctie voorkomt, moeten we de boogsecansafgeleide regel toepassen met de kettingregel om de gehele functie af te leiden. <\/p>\n<p class=\"has-text-align-center\" id=\"block-86fe6911-58a5-4f15-be8f-9e340c0a1401\"><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-8101c1f6c91528fc3a8c0a3c35509c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(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=\"439\" 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 verheven tot de macht 2 min 1: <\/p>\n<p class=\"has-text-align-center\" id=\"block-99708268-e595-48a1-8a30-244af13d52f2\"><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-13a238ac3f7cb034fec6d5ae6b5b3826_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsec}(x^4-5x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{4x^3-10x}{(x^4-5x^2)\\cdot \\sqrt{\\left(x^4-5x^2\\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 ziet u wat de afgeleide is van de boogsecant (formule). Je vindt opgeloste oefeningen voor afgeleiden van de boogsecant van een functie. Arcsecant-afgeleide formule De afgeleide van de boogsecans van x is \u00e9\u00e9n over het product van x maal de wortel van x kwadraat min 1. Daarom is de afgeleide van de &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/boogsecante-drift\/\"> <span class=\"screen-reader-text\">Arcsecante afgeleide<\/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-436","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 arcsecant - 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\/boogsecante-drift\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Afgeleide van arcsecant - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina ziet u wat de afgeleide is van de boogsecant (formule). 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Je vindt opgeloste oefeningen voor afgeleiden van de boogsecant van een functie. Arcsecant-afgeleide formule De afgeleide van de boogsecans van x is \u00e9\u00e9n over het product van x maal de wortel van x kwadraat min 1. 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