{"id":144050,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/what-is-the-derivative-of-y-coscoscosx"},"modified":"2017-08-17T11:46:14","modified_gmt":"2017-08-17T11:46:14","slug":"what-is-the-derivative-of-y-coscoscosx","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/what-is-the-derivative-of-y-coscoscosx\/","title":{"rendered":"What is the derivative of ##y = cos(cos(cos(x)))##?"},"content":{"rendered":"<p>##(dy)\/(dx)=-sin(cos(cos(x)))sin(cosx)sin(x)##<\/p>\n<p>In order to differentiate a function of a function, say ##y, =f(g(x))##, where we have to find ##(dy)\/(dx)##, we need to do (a) substitute ##u=g(x)##, which gives us ##y=f(u)##. Then we need to use a formula called , which states that ##(dy)\/(dx)=(dy)\/(du)xx(du)\/(dx)##. In fact if we have something like ##y=f(g(h(x)))##, we can have ##(dy)\/(dx)=(dy)\/(df)xx(df)\/(dg)xx(dg)\/(dh)##<\/p>\n<p>Hence for ##y=cos(cos(cos(x)))##<\/p>\n<p>##(dy)\/(dx)=-sin(cos(cos(x)))xxd\/(dx)(cos(cos(x)))##<\/p>\n<p>= ##-sin(cos(cos(x)))xx(-sin(cosx))xxd\/(dx)cos(x)##<\/p>\n<p>= ##-sin(cos(cos(x)))xx(-sin(cosx))xx-sin(x)##<\/p>\n<p>= ##-sin(cos(cos(x)))sin(cosx)sin(x)##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>##(dy)\/(dx)=-sin(cos(cos(x)))sin(cosx)sin(x)## In order to differentiate a function of a function, say ##y, =f(g(x))##, where we have to find ##(dy)\/(dx)##, we need to do (a) substitute ##u=g(x)##, which gives us ##y=f(u)##. Then we need to use a formula called , which <a href=\"https:\/\/www.benedictsol.com\/blogs\/what-is-the-derivative-of-y-coscoscosx\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-144050","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/144050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=144050"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/144050\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=144050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=144050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=144050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}