The function you are working with is: y=tan\u2061(x2+3x)y = \\tan(x^2 + 3x)y=tan(x2+3x)<\/p>\n\n\n\n
To find the derivative of this function, we need to apply the chain rule<\/strong>, which is used when differentiating compositions of functions. Here, we have two functions:<\/p>\n\n\n\n The derivative of tan\u2061(u)\\tan(u)tan(u) is: ddu(tan\u2061(u))=sec\u20612(u)\\frac{d}{du} \\left( \\tan(u) \\right) = \\sec^2(u)dud\u200b(tan(u))=sec2(u)<\/p>\n\n\n\n The derivative of x2+3xx^2 + 3xx2+3x is: ddx(x2+3x)=2x+3\\frac{d}{dx} \\left( x^2 + 3x \\right) = 2x + 3dxd\u200b(x2+3x)=2x+3<\/p>\n\n\n\n The derivative of y=tan\u2061(x2+3x)y = \\tan(x^2 + 3x)y=tan(x2+3x) with respect to xxx is: dydx=ddu(tan\u2061(u))\u22c5dudx\\frac{dy}{dx} = \\frac{d}{du} \\left( \\tan(u) \\right) \\cdot \\frac{du}{dx}dxdy\u200b=dud\u200b(tan(u))\u22c5dxdu\u200b<\/p>\n\n\n\n Substituting the derivatives from Steps 1 and 2: y\u2032=sec\u20612(x2+3x)\u22c5(2x+3)y’ = \\sec^2(x^2 + 3x) \\cdot (2x + 3)y\u2032=sec2(x2+3x)\u22c5(2x+3)<\/p>\n\n\n\n Thus, the correct derivative is: y\u2032=(2x+3)sec\u20612(x2+3x)y’ = (2x + 3) \\sec^2(x^2 + 3x)y\u2032=(2x+3)sec2(x2+3x)<\/p>\n\n\n\n The correct answer is A. y\u2032=(2x+3)sec\u20612(x2+3x)y’ = (2x + 3) \\sec^2(x^2 + 3x)y\u2032=(2x+3)sec2(x2+3x)<\/strong>.<\/p>\n\n\n\n What is the derivative of the function y = tan (x^2 + 3x). A. y’ = (2x + 3) sec^2 (x^2 + 3x) B. y’ = (2x – 3) sec^2 (x^2 + 3x) C. y’ = (2x + 3) sec^2 (x^2 – 3x) D. y’ = (2x – 3) sec^2 (x^2 – 3x) The Correct […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-258755","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258755","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=258755"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258755\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Differentiate the outer function with respect to uuu<\/h3>\n\n\n\n
Step 2: Differentiate the inner function u=x2+3xu = x^2 + 3xu=x2+3x with respect to xxx<\/h3>\n\n\n\n
Step 3: Apply the chain rule<\/h3>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
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