{"id":18691,"date":"2016-11-14T17:40:17","date_gmt":"2016-11-14T17:40:17","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=18691"},"modified":"2016-11-14T17:40:17","modified_gmt":"2016-11-14T17:40:17","slug":"calculus-proving-derivative-of-tan-quotient-rule","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-proving-derivative-of-tan-quotient-rule\/","title":{"rendered":"Calculus: proving derivative of tan: quotient rule"},"content":{"rendered":"

The tutor shows how to remind yourself that the derivative of tanx is sec2<\/sup>x.<\/h1>\n

Let’s imagine you don’t recall that (tanx)’=sec2<\/sup>x. Here’s how to reconstruct it:<\/p>\n

    \n
  1. \nRecall that tanx=sinx\/cosx<\/li>\n
  2. Take the derivative of sinx\/cosx using the quotient rule:(u\/v)’ = (vu’-uv’)\/v2<\/sup><\/li>\n
  3. In this case, (sinx\/cosx)’ = [cosx(cosx) – sinx(-sinx)]\/cos2<\/sup>x<\/li>\n
  4. Recall that cos2<\/sup>x +sin2<\/sup>x = 1.\n
  5. Simplifying we arrive at (sinx\/cosx)’ = 1\/cos2<\/sup>x = sec2<\/sup>x<\/li>\n<\/ol>\n

    Therefore, (tanx)’=(sinx\/cosx)’=sec2<\/sup>x.<\/p>\n

    Source:<\/p>\n

    Larson, Roland and Robert Hostetler. Calculus<\/u>, part one. Toronto: D C Heath and Company, 1989.<\/p>\n

    Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

    The tutor shows how to remind yourself that the derivative of tanx is sec2x. Let’s imagine you don’t recall that (tanx)’=sec2x. Here’s how to reconstruct it: Recall that tanx=sinx\/cosx Take the derivative of sinx\/cosx using the quotient rule:(u\/v)’ = (vu’-uv’)\/v2 …<\/p>\n

    Calculus: proving derivative of tan: quotient rule<\/span> Read More »<\/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":[2022,2021],"class_list":["post-18691","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-differentiate-tanx","tag-quotient-rule"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18691","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=18691"}],"version-history":[{"count":13,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18691\/revisions"}],"predecessor-version":[{"id":18704,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18691\/revisions\/18704"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=18691"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=18691"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=18691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}