{"id":47233,"date":"2024-05-06T15:38:55","date_gmt":"2024-05-06T15:38:55","guid":{"rendered":"https:\/\/www.oracletutoring.ca\/blog\/?p=47233"},"modified":"2024-05-06T15:38:55","modified_gmt":"2024-05-06T15:38:55","slug":"calculus-why-the-derivative-of-tanx-is-secx2","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-why-the-derivative-of-tanx-is-secx2\/","title":{"rendered":"Calculus: why the derivative of tanx is (secx)^2"},"content":{"rendered":"\n<h2>Tutoring calculus, everyday formulas students count on can often be verified. The tutor mentions the derivative of tanx.<\/h2>\n<p>\nIt&#8217;s true that (tanx)&#8217; = (secx)^2. But why?<\/p>\n<p>\nRealizing tanx = sinx\/cosx, then using the the quotient rule (u\/v)&#8217; = (vu&#8217; &#8211; uv&#8217;)\/v^2, we get<\/p>\n<p>\n(sinx\/cosx)&#8217; = (cosx*cosx &#8211; sinx(-sinx))\/(cosx)^2<\/p>\n<p>\ncosx*cosx + sinx*sinx = 1, giving<\/p>\n<p>\n(sinx\/cosx)&#8217; = 1\/(cosx)^2 = (secx)^2<\/p>\n<p>\nSource:<\/p>\n<p>\nLarson, Roland E. and Robert P. Hostetler. <em>Calculus.<\/em> Toronto: D C Heath and Company, 1989.<\/p>\nJack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":"<p>Tutoring calculus, everyday formulas students count on can often be verified. The tutor mentions the derivative of tanx. It&#8217;s true that (tanx)&#8217; = (secx)^2. But why? Realizing tanx = sinx\/cosx, then using the the quotient rule (u\/v)&#8217; = (vu&#8217; &#8211; &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-why-the-derivative-of-tanx-is-secx2\/\"> <span class=\"screen-reader-text\">Calculus: why the derivative of tanx is (secx)^2<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234],"tags":[1146,2021,3136,3137],"class_list":["post-47233","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-derivative","tag-quotient-rule","tag-trig-derivatives","tag-verifying-differentiation-formula"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=47233"}],"version-history":[{"count":1,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47233\/revisions"}],"predecessor-version":[{"id":47234,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/47233\/revisions\/47234"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=47233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=47233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=47233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}