The derivative of y = arcsin(3x) is given by<\/p>\n
##y’=3\/(sqrt(1-9x^2)##<\/p>\n
The rule for the derivative of f(x) = arcsin(x) is<\/p>\n
##f'(x) = 1\/(sqrt(1-x^2)##<\/p>\n
However, in this instance, we are dealing with a composite function (a function of another function of x) and we have to use the as well.<\/p>\n
So the rule for the derivative of h(x) = arcsin f(x) is given by<\/p>\n
##h'(x)=(f'(x))\/(sqrt(1-(f(x))^2)##<\/p>\n
In our case f(x) = 3x, so f'(x) = 3 and ##(f(x))^2=9x^2##<\/p>\n
Substituting, we get <\/p>\n
##h'(x)=3\/(sqrt(1-9x^2)##<\/p>\n","protected":false},"excerpt":{"rendered":"
The derivative of y = arcsin(3x) is given by ##y’=3\/(sqrt(1-9x^2)## The rule for the derivative of f(x) = arcsin(x) is ##f'(x) = 1\/(sqrt(1-x^2)## However, in this instance, we are dealing with a composite function (a function of another function of 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":[],"tags":[],"class_list":["post-72067","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/72067","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=72067"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/72067\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=72067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=72067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=72067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}