{"id":143539,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/how-do-you-find-the-derivative-of-sinx3"},"modified":"2017-08-17T11:42:54","modified_gmt":"2017-08-17T11:42:54","slug":"how-do-you-find-the-derivative-of-sinx3","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/how-do-you-find-the-derivative-of-sinx3\/","title":{"rendered":"How do you find the derivative of ##sin(x^3)##?"},"content":{"rendered":"<p>Using the notation provided there, if we define ##y(x) = sin(x^3)## and ##u=x^3##, we may rewrite ##y(x)## as ##y(u)=sin(u)##<\/p>\n<p>From the chain rule we know that ##dy\/dx = (du)\/dx (dy)\/(du)##. Recall that ##u(x) = x^3## and ##y(u) = sin(u)##. Therefore, by the , ##(du)\/dx = 3x^2##, and by the definitions of trigonometric derivatives, ##dy\/(du) = cos(u)##. Thus:<\/p>\n<p>##dy\/dx = (3x^2)(cos (u)) ##<\/p>\n<p>Substituting ##x^3## back for u yields:<\/p>\n<p>##dy\/dx = 3x^2 cos(x^3)##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using the notation provided there, if we define ##y(x) = sin(x^3)## and ##u=x^3##, we may rewrite ##y(x)## as ##y(u)=sin(u)## From the chain rule we know that ##dy\/dx = (du)\/dx (dy)\/(du)##. Recall that ##u(x) = x^3## and ##y(u) = sin(u)##. Therefore, <a href=\"https:\/\/www.benedictsol.com\/blogs\/how-do-you-find-the-derivative-of-sinx3\/\" 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-143539","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143539","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=143539"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143539\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=143539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=143539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=143539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}