{"id":55105,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/what-is-the-derivative-of-ln-e2x-2"},"modified":"2017-08-16T13:19:13","modified_gmt":"2017-08-16T13:19:13","slug":"what-is-the-derivative-of-ln-e2x-2","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/what-is-the-derivative-of-ln-e2x-2\/","title":{"rendered":"What is the derivative of ##ln e^(2x)##?"},"content":{"rendered":"<p>##y=ln(u)##<\/p>\n<p>##:. dy\/(du)=1\/u=1\/(e^(2x))##<\/p>\n<p>##u=e^(2x)##, ##:. (du)\/(dx)=2e^(2x)##<\/p>\n<p>Now, using the &#8230;<\/p>\n<p>##(dy)\/(du)*(du)\/(dx)=1\/(e^(2x))*2e^(2x)=2##<\/p>\n<p>##:. (dy)\/(dx)=2##<\/p>\n<p>This all worked because:<\/p>\n<p>When ##y=e^(f(x))##<\/p>\n<p>##(dy)\/(dx)=f'(x)e^(f(x))##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>##y=ln(u)## ##:. dy\/(du)=1\/u=1\/(e^(2x))## ##u=e^(2x)##, ##:. (du)\/(dx)=2e^(2x)## Now, using the &#8230; ##(dy)\/(du)*(du)\/(dx)=1\/(e^(2x))*2e^(2x)=2## ##:. (dy)\/(dx)=2## This all worked because: When ##y=e^(f(x))## ##(dy)\/(dx)=f'(x)e^(f(x))##<\/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-55105","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/55105","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=55105"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/55105\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=55105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=55105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=55105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}