{"id":428,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","guid":{"rendered":"https:\/\/mathority.org\/nl\/larccosinederivaat\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"larccosinederivaat","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/larccosinederivaat\/","title":{"rendered":"Afgeleide van boogcosinus"},"content":{"rendered":"<p>Hier leggen we uit hoe je de arccosinus van een functie kunt afleiden. Daarnaast vind je voorbeelden van afgeleiden van de boogcosinus en kun je oefenen met stap voor stap opgeloste oefeningen. Ten slotte laten we u het bewijs zien van de arccosine-afgeleide formule. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span> Wat is de afgeleide van boogcosinus?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de arccosinus van x is negatief \u00e9\u00e9n over de vierkantswortel van \u00e9\u00e9n minus x kwadraat.<\/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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Daarom is de <strong>afgeleide van de arccosinus van een functie<\/strong> gelijk aan minus het quoti\u00ebnt van de afgeleide van die functie gedeeld door de vierkantswortel van \u00e9\u00e9n minus het kwadraat van die 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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> In feite wordt de eerste formule verkregen door x in de tweede formule te vervangen door u. Samenvattend: de formule voor de afgeleide van de inverse cosinus is: <\/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-arc-cosinus.webp\" alt=\"boogcosinusafgeleide\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Zoals je kunt zien, is de formule voor de afgeleide van arccosinus hetzelfde als de <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/nl\/larcosinederivaat\/\">afgeleide van arcsinus<\/a><\/span> , maar met een negatief ervoor. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span> Voorbeelden van de boogcosinusderivaat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Gegeven de formule voor de afgeleide van de arccosinusfunctie, zullen we nu verschillende voorbeelden van dit soort trigonometrische derivaten analyseren. Op deze manier wordt het gemakkelijker voor u om te begrijpen hoe de boogcosinus van een functie wordt afgeleid. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcocoseno-de-2x\"><\/span> Voorbeeld 1: Afgeleide van de boogcosinus van 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-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Om de afgeleide van de boogcosinus op te lossen, gebruiken we de formule:<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> De afgeleide van 2x is 2, dus de boogcosinusafgeleide van 2x is negatief 2 over de wortel \u00e9\u00e9n minus 2x 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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\sqrt{1-(2x)^2}}=-\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"576\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span> Voorbeeld 2: Afgeleide van de boogcosinus van x kwadraat<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-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> We passen de arccosine-afgeleide formule toe met de kettingregel om de afgeleide te berekenen:<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Omdat de afgeleide van de functie x <sup>2<\/sup> 2x is, is de afgeleide van de boogcosinus van x tot de macht van 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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=-\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"565\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcocoseno-de-un-logaritmo\"><\/span> Voorbeeld 3: Afgeleide van de arccosinus van een logaritme<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-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> De functie in dit voorbeeld is een functie die is samengesteld uit een arccosinus en een natuurlijke logaritme, dus we moeten de kettingregel gebruiken om deze af te leiden.<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> De afgeleide van de natuurlijke logaritme is \u00e9\u00e9n gedeeld door x, daarom is de afgeleide van de gehele 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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcocoseno\"><\/span> Arccosinederivaat loste problemen op<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Leid de volgende arccosinusfuncties 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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" 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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" 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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" style=\"vertical-align: -7px;\"><\/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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" style=\"vertical-align: -20px;\"><\/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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" style=\"vertical-align: -20px;\"><\/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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" 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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" 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-d1a362c38a56084dec3c6ebbccba9ab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =-\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=-\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=-\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"267\" 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-del-arcocoseno\"><\/span> Bewijs van de afgeleide formule van de boogcosinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> In deze sectie zullen we de formule demonstreren voor de afgeleide van boogcosinus.<\/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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Eerst transformeren we boogcosinus naar cosinus:<\/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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> We leiden nu de twee kanten van de gelijkheid 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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Wij zuiveren u:<\/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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> We gebruiken de fundamentele trigonometrische identiteit om sinus in cosinus te veranderen:<\/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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" style=\"vertical-align: -6px;\"><\/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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Maar hierboven hebben we afgeleid dat x gelijk is aan de cosinus van y, dus de vergelijking blijft:<\/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-8c3b21ba43e58ec763ab27498aa4fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> En zo kwamen we bij de uitdrukking voor de afgeleide van de boogcosinus, dus de formule wordt gedemonstreerd.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hier leggen we uit hoe je de arccosinus van een functie kunt afleiden. Daarnaast vind je voorbeelden van afgeleiden van de boogcosinus en kun je oefenen met stap voor stap opgeloste oefeningen. Ten slotte laten we u het bewijs zien van de arccosine-afgeleide formule. Wat is de afgeleide van boogcosinus? De afgeleide van de arccosinus &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/larccosinederivaat\/\"> <span class=\"screen-reader-text\">Afgeleide van boogcosinus<\/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-428","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 boogcosinus - 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\/larccosinederivaat\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Afgeleide van boogcosinus - Mathority\" \/>\n<meta property=\"og:description\" content=\"Hier leggen we uit hoe je de arccosinus van een functie kunt afleiden. Daarnaast vind je voorbeelden van afgeleiden van de boogcosinus en kun je oefenen met stap voor stap opgeloste oefeningen. Ten slotte laten we u het bewijs zien van de arccosine-afgeleide formule. Wat is de afgeleide van boogcosinus? 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