{"id":143458,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/how-do-you-derive-ytanx-using-the-definition-of-the-derivative"},"modified":"2017-08-17T11:42:27","modified_gmt":"2017-08-17T11:42:27","slug":"how-do-you-derive-ytanx-using-the-definition-of-the-derivative","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/how-do-you-derive-ytanx-using-the-definition-of-the-derivative\/","title":{"rendered":"How do you derive y=tanx using the definition of the derivative?"},"content":{"rendered":"<p>Use the tangent of a sum, continuity of tangent and ##lim_(hrarr0)tan h\/h = 1##<\/p>\n<p>##f(x) = tanx##<\/p>\n<p>##f'(x) = lim_(hrarr0)(tan(x+h) &#8211; tanx)\/h##<\/p>\n<p>## = lim_(hrarr0)((tanx+tan h)\/(1-tanxtan h) &#8211; tanx)\/h##<\/p>\n<p>## = lim_(hrarr0)(tanx+tan h- tanx+tan^2xtan h)\/(h(1-tanxtan h)) ##<\/p>\n<p>## = lim_(hrarr0)(tan h\/h * (1+tan^2x)\/(1-tanxtan h)) ##<\/p>\n<p>## = (1) * (1+tan^2x)\/(1-0) = 1+tan^2x = sec^2x##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Use the tangent of a sum, continuity of tangent and ##lim_(hrarr0)tan h\/h = 1## ##f(x) = tanx## ##f'(x) = lim_(hrarr0)(tan(x+h) &#8211; tanx)\/h## ## = lim_(hrarr0)((tanx+tan h)\/(1-tanxtan h) &#8211; tanx)\/h## ## = lim_(hrarr0)(tanx+tan h- tanx+tan^2xtan h)\/(h(1-tanxtan h)) ## ## = lim_(hrarr0)(tan <a href=\"https:\/\/www.benedictsol.com\/blogs\/how-do-you-derive-ytanx-using-the-definition-of-the-derivative\/\" 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-143458","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143458","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=143458"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143458\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=143458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=143458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=143458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}