{"id":84,"date":"2023-09-17T10:58:44","date_gmt":"2023-09-17T10:58:44","guid":{"rendered":"https:\/\/mathority.org\/nl\/afgeleide-van-de-secans\/"},"modified":"2023-09-17T10:58:44","modified_gmt":"2023-09-17T10:58:44","slug":"afgeleide-van-de-secans","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/afgeleide-van-de-secans\/","title":{"rendered":"Afgeleide van de secans"},"content":{"rendered":"<p>Hier ontdekt u hoe u de secans van een functie kunt afleiden. Bovendien kunt u stap voor stap verschillende oefeningen zien die zijn opgelost op de afgeleide van de secans. En tot slot vind je de demonstratie van de formule voor dit type trigonometrische afgeleide. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-la-secante\"><\/span> Wat is de afgeleide van de secans?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>De afgeleide van de secans van x is gelijk aan het product van de secans van x en de tangens 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-96448e16137a4b0d5cda8192ec339ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"434\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Door trigonometrische formules toe te passen, kan de afgeleide van de secans van x ook worden gedefinieerd als het quoti\u00ebnt van de sinus van x gedeeld door het kwadraat van de cosinus 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-7055796dc0e57b6284a41ca70ecca764_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)=\\cfrac{1}{\\text{cos}(x)}\\cdot \\cfrac{\\text{sen}(x)}{\\text{cos}(x)}=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"390\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> En als we de kettingregel toepassen, is de <strong>afgeleide van de secans van een functie<\/strong> het product van de secans van de functie maal de tangens van de functie maal de afgeleide 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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Samenvattend is de formule voor de afgeleide van de secansfunctie 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-secante.webp\" alt=\"afgeleid van de secans\" class=\"wp-image-2351\" width=\"475\" height=\"314\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-secante\"><\/span> Voorbeelden van afgeleide van de secans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Zodra we hebben gezien wat de formule voor de afgeleide van de secans is, zullen we verschillende voorbeelden van dit soort trigonometrische derivaten oplossen. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-secante-de-2x\"><\/span> Voorbeeld 1: Afgeleide van de secans van 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> In dit voorbeeld zullen we zien hoeveel de afgeleide van de secans van 2x waard 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-c8a3b19bc9ee15896b5416920d623745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Om de secans van de functie 2x af te leiden, moet u de bijbehorende formule gebruiken. Bovendien hebben we in het secansargument een andere functie dan x, dus moeten we de kettingregel 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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De functie 2x is lineair, dus de afgeleide ervan is 2. Om de afgeleide te vinden, vervangen we daarom eenvoudigweg de u door 2x en de u&#8217; door 2 in 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-2decb8aff43ac88c25cae4f6c1443b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(2x)\\cdot \\text{tan}(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"482\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-secante-de-x-al-cuadrado\"><\/span> Voorbeeld 2: Afgeleide van de secans van x kwadraat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> In deze oefening zullen we zien wat de afgeleide is van de secans 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-e1359b6d31f1ec6172c29ec2066b3fb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Om de secans van een functie af te leiden, kun je een van de twee formules hierboven gebruiken, maar in dit geval zullen we de functie differenti\u00ebren met de formule voor vermenigvuldiging tussen de secans en de raaklijn.<\/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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De afgeleide van x tot de macht 2 geeft 2x, dus de afgeleide van de secans van x in het kwadraat 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-2e0bdd83c01111c51620bd6a558a5930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x^2)\\cdot \\text{tan}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"490\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-secante-al-cubo-de-un-polinomio\"><\/span> Voorbeeld 3: Afgeleide van de secanskubus van een polynoom<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-6ee68247e5fd1854b875d655b1615701_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}^3(x^5+4x^2-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> De regel voor de afgeleide van de secans 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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Maar in dit geval moeten we een samengestelde functie afleiden, aangezien de secans tot de derde macht wordt verheven en bovendien hebben we in zijn argumentatie een polynomiale functie. Om de hele functie te differenti\u00ebren, moeten we dus de kettingregel 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-7ab88cc23ab3fb559e2386cd52637082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =3\\text{sec}^2(x^5+4x^2-3)\\text{sec}(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\\\[1.5ex]&amp;=3\\text{sec}^3(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"562\" 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-una-secante\"><\/span> Opgeloste oefeningen op de afgeleide van een secans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Leid de volgende secansfuncties 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-a63efa4ccc6266dc6db9552b5663ccb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"186\" 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-d4cd03385df118ead733c64d1524bb36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{sec}^4(5x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" 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-6b8e0ec036c5a0ccaca77d1116a2606a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"159\" 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-787d864c315ebf629c2505df13cfdf70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"178\" style=\"vertical-align: -11px;\"><\/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-1e9e9e0065335901bb018afd8458bf7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"187\" 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 de 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-c162c3a202d8d10ed26b6f5ad4afe7f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\\cdot \\text{tan}(x^6-6x^3)\\cdot (6x^5-18x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"415\" 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-72985d8bce95d808b9070bc7b834b271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{B) }f(x)&amp; =4\\text{sec}^3(5x^4)\\cdot \\text{sec}(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\\\[1.5ex] &amp;=4\\text{sec}^4(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"366\" 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-1a89fb7e8b228b31af9979a4fc0b08ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\\cdot \\text{tan}\\bigl(\\ln(x)\\bigr)\\cdot \\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"281\" style=\"vertical-align: -12px;\"><\/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-7a488bce8bdd2cb66ebb028ca017f172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\\cdot \\text{tan}\\left(e^{x^2+3x}\\right)\\cdot e^{x^2+3x}\\cdot (2x+3)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"429\" style=\"vertical-align: -11px;\"><\/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-b1bb860fafc464f3c8a30bf3e9b29a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\\cdot \\text{tan}\\left(\\sqrt{5x+1}\\right)\\cdot \\cfrac{5}{2\\sqrt{5x+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"400\" style=\"vertical-align: -16px;\"><\/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-secante\"><\/span> Demonstratie van de formule voor de afgeleide van de secans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Vervolgens zullen we de formule voor de afgeleide van de secans bewijzen. Hoewel het uiteraard niet nodig is om het bewijs uit je hoofd te kennen, is het altijd goed om te begrijpen waar de formules vandaan komen.<\/p>\n<p> Wiskundig gezien is de definitie van de secans de multiplicatieve inverse van de 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-8e3493c8e50b7c4b713b7c0f6ea9eca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x)=\\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"178\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Daarom kunnen we proberen de secans af te leiden 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-37c02387c22125a313ff7fe65c1a7b37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"121\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> En zoals we in de eerste sectie hebben gezien, kan de vorige uitdrukking worden omgezet in de formule voor de afgeleide van de secans. Om dit te doen, scheiden we de breuk in twee verschillende breuken:<\/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-eb2f40cc564d430340271ea1b7659084_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> De deling van de sinus door de cosinus is equivalent aan de raaklijn, daarom vervangen we het genoemde quoti\u00ebnt door de raaklijn:<\/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-3ce86a0b57ad6e2322c169eb90d9e8bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Volgens de wiskundige definitie van de secansfunctie is de cosinus de inverse vermenigvuldiger. Dus door \u00e9\u00e9n gedeeld door de cosinus te vervangen door de secans, komen we tot de formule voor de afgeleide ervan:<\/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-d0ea3bb9b42cd0a3474363910fee95bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\text{sec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hier ontdekt u hoe u de secans van een functie kunt afleiden. Bovendien kunt u stap voor stap verschillende oefeningen zien die zijn opgelost op de afgeleide van de secans. En tot slot vind je de demonstratie van de formule voor dit type trigonometrische afgeleide. Wat is de afgeleide van de secans? De afgeleide van &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/afgeleide-van-de-secans\/\"> <span class=\"screen-reader-text\">Afgeleide van de secans<\/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-84","post","type-post","status-publish","format-standard","hentry","category-derivaten"],"yoast_head":"<!-- This site is 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