{"id":4296,"date":"2022-06-11T07:09:18","date_gmt":"2022-06-11T07:09:18","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4296"},"modified":"2022-06-11T07:09:18","modified_gmt":"2022-06-11T07:09:18","slug":"derivatives-of-composite-functions","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/11\/derivatives-of-composite-functions\/","title":{"rendered":"Derivatives of Composite Functions"},"content":{"rendered":"\n<p>If f and g are the derivative functions in their domain, then f(g(x) is also differentiable. This is known as the\u00a0chain rule\u00a0of differentiation used for\u00a0composite functions. (fog)'(x) = f'[(g(x)] g'(x). This also can be written as y = f(u) and t = g(x) , then dy\/dx = dy\/ dt . dt\/dx<\/p>\n\n\n\n<p>For example, consider y = tan<sup>2<\/sup>x. This is a composite function. By the chain rule, y = u<sup>2&nbsp;<\/sup>, where u = tan x<\/p>\n\n\n\n<p>du\/dt = 2u<\/p>\n\n\n\n<p>dy\/du = d\/dx .tan x = sec&nbsp;<sup>2<\/sup>&nbsp;x<\/p>\n\n\n\n<p>dy\/dx = dy\/du . du\/dx<\/p>\n\n\n\n<p>= 2 u . sec&nbsp;<sup>2<\/sup>&nbsp;x<\/p>\n\n\n\n<p>= 2 tan x. sec&nbsp;<sup>2<\/sup>&nbsp;x<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If f and g are the derivative functions in their domain, then f(g(x) is also differentiable. This is known as the\u00a0chain rule\u00a0of differentiation used for\u00a0composite functions. (fog)'(x) = f'[(g(x)] g'(x). This also can be written as y = f(u) and t = g(x) , then dy\/dx = dy\/ dt . dt\/dx For example, consider y [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[799],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4296"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4296"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4296\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}