{"id":440,"date":"2023-07-03T02:54:42","date_gmt":"2023-07-03T02:54:42","guid":{"rendered":"https:\/\/mathority.org\/nl\/afgeleide-van-de-hyperbolische-cosecans\/"},"modified":"2023-07-03T02:54:42","modified_gmt":"2023-07-03T02:54:42","slug":"afgeleide-van-de-hyperbolische-cosecans","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/afgeleide-van-de-hyperbolische-cosecans\/","title":{"rendered":"Afgeleide van de hyperbolische cosecans"},"content":{"rendered":"<p>In dit artikel leggen we uit hoe je de hyperbolische cosecans van een functie kunt afleiden. Bovendien zult u verschillende opgeloste voorbeelden kunnen zien van de afgeleide van de hyperbolische cosecans. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante-hiperbolica\"><\/span> Formule voor de afgeleide van de hyperbolische cosecans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de hyperbolische cosecans van x is gelijk aan minus de hyperbolische cosecans van x maal de hyperbolische cotangens van 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-b2fef8fd91e2354a27e8902e390ddabf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x)\\cdot \\text{cotgh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"517\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Daarom is de <strong>afgeleide van de hyperbolische cosecans van een functie<\/strong> minus het product van de hyperbolische cosecans van de functie maal de hyperbolische cotangens van de functie maal de afgeleide van de genoemde functie.<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kort gezegd is de formule voor het afleiden van de cosecans van een functie: <\/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-cosecante-hyperbolique.webp\" alt=\"afgeleid van de hyperbolische cosecans\" class=\"wp-image-2761\" width=\"505\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> In feite komen de voorgaande twee uitdrukkingen overeen met \u00e9\u00e9n enkele formule, het verschil is dat in de tweede formule de kettingregel wordt toegepast. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante-hiperbolica\"><\/span> Voorbeelden van afgeleide van de hyperbolische cosecans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nadat we hebben gezien wat de formule is voor de afgeleide van de hyperbolische cosecans, volgen hier verschillende uitgewerkte voorbeelden van dit type trigonometrische afgeleide.<\/p>\n<h3 class=\"wp-block-heading\"> voorbeeld 1<\/h3>\n<p> In dit eerste voorbeeld zullen we de hyperbolische cosecans van x kwadraat 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-24a7761cd3b41af2f9802ef84f616047_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De functie van het argument van de hyperbolische cosecans is anders dan x, dus we moeten de formule gebruiken voor de afgeleide van de hyperbolische cosecans met de kettingregel.<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dus om deze trigonometrische functie af te leiden, hoeven we alleen maar de waarden in de vorige formule te vervangen, dat wil zeggen dat we in het argument van de hyperbolische cosecans en de hyperbolische tangens x <sup>2<\/sup> plaatsen, en we vermenigvuldigen alles met de afgeleide van x kwadraat, wat 2x is: <\/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-068551500cf0689b8d21dcb83f0b6bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x^2)\\cdot \\text{cotgh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"573\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Voorbeeld 2<\/h3>\n<p> In deze oefening zullen we zien hoeveel de afgeleide is van de hyperbolische cosecans van x in de derde macht:<\/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-38165f7bf2e567bb8bab90ba80cf3c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Om de afgeleide van de hyperbolische cosecans van een functie te vinden, passen we de formule toe:<\/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-880e801fc4e1c9f3fce3d7fb031d4e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(u)\\cdot \\text{cotgh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"545\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De afgeleide van x in de derde macht is 3x <sup>2<\/sup> , dus de afgeleide van de gehele functie is: <\/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-b88f49530fdce04138277673f41d2457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosech}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{cosech}(x^3)\\cdot \\text{cotgh}(x^3)\\cdot 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"580\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel leggen we uit hoe je de hyperbolische cosecans van een functie kunt afleiden. Bovendien zult u verschillende opgeloste voorbeelden kunnen zien van de afgeleide van de hyperbolische cosecans. Formule voor de afgeleide van de hyperbolische cosecans De afgeleide van de hyperbolische cosecans van x is gelijk aan minus de hyperbolische cosecans van &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/afgeleide-van-de-hyperbolische-cosecans\/\"> <span class=\"screen-reader-text\">Afgeleide van de hyperbolische cosecans<\/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-440","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 hyperbolische cosecans - 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\/afgeleide-van-de-hyperbolische-cosecans\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Afgeleide van de hyperbolische cosecans - Mathority\" \/>\n<meta property=\"og:description\" content=\"In dit artikel leggen we uit hoe je de hyperbolische cosecans van een functie kunt afleiden. 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