{"id":435,"date":"2023-07-03T07:22:34","date_gmt":"2023-07-03T07:22:34","guid":{"rendered":"https:\/\/mathority.org\/nl\/is-afgeleid-van-de-cosecans\/"},"modified":"2023-07-03T07:22:34","modified_gmt":"2023-07-03T07:22:34","slug":"is-afgeleid-van-de-cosecans","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/is-afgeleid-van-de-cosecans\/","title":{"rendered":"Afgeleide van de cosecans"},"content":{"rendered":"<p>In dit artikel leggen we uit hoe je de cosecans van een functie (formule) kunt afleiden. Je vindt er ook stap voor stap opgeloste oefeningen voor de afgeleide van de cosecant. En tot slot zul je de demonstratie van de formule voor dit type trigonometrische afgeleide kunnen zien. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante\"><\/span> Cosecant-afgeleide formule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de cosecans van x is gelijk aan minus het quoti\u00ebnt van de cosinus van x gedeeld door de vierkante sinus 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-19e966c85664331b8b6c87860849678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Met behulp van goniometrische formules kunnen we ook de afgeleide van de cosecans van x defini\u00ebren als minus het product van de cotangens van x maal de cosecans van 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-e66d4cc483a3f2c40401bf2e34fa54c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}=-\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\\cdot \\cfrac{1}{\\text{sen}(x)}=-\\text{cot}(x)\\cdot \\text{cosec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> En als we de kettingregel toepassen, is de <strong>afgeleide van de cosecans van een functie<\/strong> minus het product van de afgeleide van de functie maal de cosinus van de functie, gedeeld door de kwadratische sinus van de functie.<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> De formule die wordt gebruikt om de cosecans van een functie af te leiden is daarom als volgt: <\/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\/derive-de-la-formule-cosecante.webp\" alt=\"afgeleid van de cosecansformule\" class=\"wp-image-2527\" width=\"398\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante\"><\/span> Voorbeelden van afgeleide van de cosecans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nu we hebben gezien wat de formule voor de afgeleide van de cosecans is, zullen we nu verschillende voorbeelden geven. Je kunt dus precies zien hoe de cosecans van een functie wordt afgeleid. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cosecante-de-2x\"><\/span> Voorbeeld 1: Afgeleide van de cosecans van 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> In dit voorbeeld zullen we zien hoeveel de afgeleide is van de cosecans van 2x:<\/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-44aef07389e7b7d69f4ecf9e46660838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De cosecans-argumentfunctie verschilt van x, dus we moeten de cosecans-afgeleide regel gebruiken met de kettingregel.<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dus om de afgeleide van deze trigonometrische functie te vinden, vervangt u eenvoudigweg de waarden in de vorige formule: in het cosinus- en sinusargument plaatsen we 2x, en u&#8217; komt overeen met de afgeleide van 2x, dat wil zeggen 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-8607025c53ca3c1a2c5e05e908d61bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2\\cdot \\text{cos}(2x)}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cosecante-de-x-al-cuadrado\"><\/span> Voorbeeld 2: Afgeleide van de cosecans van x kwadraat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> In deze oefening zullen we zien hoeveel de afgeleide is van de cosecans van x in het kwadraat:<\/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-dc9de51c8f24850940b40de616428dd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logischerwijs wordt de afgeleide van deze trigonometrische functie opgelost met behulp van de formule voor de afgeleide van de cosecans:<\/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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> De afgeleide van x in het kwadraat geeft 2x, dus de afgeleide van de cosecans van x tot de macht van twee 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-0a6b69e1f9851904ec2fc68bffeedc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x\\cdot \\text{cos}(x^2)}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cosecante-al-cubo-de-una-funcion-exponencial\"><\/span> Voorbeeld 3: Afgeleide van de derde machtssecans van een exponenti\u00eble functie<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-8bd5c47e8cd53ab52d3d30f55f898490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}^3(e^{5x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Wat het argument van de functie ook is, de regel voor de afgeleide van de cosecans van een 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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Maar in dit geval hebben we een samengestelde functie, omdat de cosecans wordt verhoogd tot drie en bovendien is er in zijn argumentatie een exponenti\u00eble functie. Om de hele functie te differenti\u00ebren, moeten we de kettingregel dus verschillende keren toepassen: <\/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-9ac2ce49dfcba1b7f27696dba0a2decb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle f'(x)&amp; = 3\\text{cosec}^2(e^{5x})\\cdot\\left(-\\frac{5e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\right)\\\\[1.5ex]&amp;=-\\frac{-15\\text{cosec}^2(e^{5x})\\cdot e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-cosecante\"><\/span> Opgeloste problemen van de afgeleide van de cosecant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Leid de volgende cosecante functies af: <\/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-9929e2437b0ed56c3510e3e0e66745c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{cosec}(x^4-2x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-90abcf0539f30dc6fc72414bfc74510f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{cosec}(x^3+e^x-10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"232\" 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-86a2ea6229cced9086f8baba7afd49dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cosec}\\bigl(\\ln(x^3+7x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" style=\"vertical-align: -7px;\"><\/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-45cdf124149223f4a3bec4984dc3ad3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{cosec}\\bigl(\\text{arccos}(x^7)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"217\" style=\"vertical-align: -7px;\"><\/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-45ae6ef998d8ab0c30309fe521b0bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{cosec}\\left(\\sqrt{9x^2-4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"226\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>zie oplossing<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fb207498fc67f62e6c30a0baecc9549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f('x)=-\\cfrac{(4x^3-4x)\\cdot \\text{cos}(x^4-2x^2)}{\\text{sen}^2(x^4-2x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"303\" 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-d42a3db78890f44f3cac95685ab9362e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f('x)=-\\cfrac{(3x^2+e^x)\\cdot \\text{cos}(x^3+e^x-10)}{\\text{sen}^2(x^3+e^x-10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"329\" 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-32dde68d2a11ef6a05d483b26f0a98ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp; =-\\cfrac{\\cfrac{3x^2+14x}{x^3+7x^2}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{\\cfrac{3x+14}{x^2+7x}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{(3x+14)\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{(x^2+7x)\\cdot \\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"333\" style=\"vertical-align: 0px;\"><\/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-b2bea25dae467cefdcc1bd48e8d9bc88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp; =-\\cfrac{-\\cfrac{7x^6}{\\sqrt{1-\\left(x^7\\right)^2}}\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =-\\cfrac{(-7x^6)\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =\\cfrac{7x^6\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"240\" width=\"348\" style=\"vertical-align: 0px;\"><\/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-eb70e1d7b6f2ce2636934b235904861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\text{E) }f'(x)&amp; =-\\cfrac{\\cfrac{18x-4}{2\\cdot\\sqrt{9x^2-4x}} \\cdot \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{\\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)}\\\\[1.5ex] &amp;=-\\cfrac{(18x-4)\\cdot  \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{2\\sqrt{9x^2-4x}\\cdot \\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"352\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-de-la-cosecante\"><\/span> Bewijs van de formule voor de afgeleide van de cosecant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Vervolgens zullen we de formule demonstreren voor de afgeleide van de cosecans. In tegenstelling tot andere demonstraties zullen we in dit geval niet de limiet gebruiken die een afgeleide definieert, maar zullen we uitgaan van de wiskundige definitie van de cosecans.<\/p>\n<p> Algebra\u00efsch is de cosecante trigonometrische functie de multiplicatieve inverse van sinus:<\/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-6ac8ff987dcebfb971915b090d8dc455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x)=\\cfrac{1}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> We kunnen daarom de afgeleide van de cosecans nemen met behulp van de quoti\u00ebntregel:<\/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-956e802336ed97943a839dbc059a168a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{0\\cdot \\text{sen}(x)-1\\cdot \\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"227\" 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-d26ab733704d285da0ec63f0901330b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Zoals je kunt zien, komen we alleen door de regel voor de afgeleide van een deling toe te passen tot de formule voor de afgeleide van de cosecans. En aangezien de afgeleide van een quoti\u00ebnt al bewezen is (je kunt het zien in de volgende link), is de cosecante afgeleide regel ook bewezen.<\/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-een-delingsquotient\/\">bewijs van de afgeleide van een quoti\u00ebnt<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel leggen we uit hoe je de cosecans van een functie (formule) kunt afleiden. Je vindt er ook stap voor stap opgeloste oefeningen voor de afgeleide van de cosecant. En tot slot zul je de demonstratie van de formule voor dit type trigonometrische afgeleide kunnen zien. Cosecant-afgeleide formule De afgeleide van de cosecans &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/is-afgeleid-van-de-cosecans\/\"> <span class=\"screen-reader-text\">Afgeleide van de 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-435","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 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\/is-afgeleid-van-de-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 cosecans - Mathority\" \/>\n<meta property=\"og:description\" content=\"In dit artikel leggen we uit hoe je de cosecans van een functie (formule) kunt afleiden. 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