How do you differentiate #f(x) = tan(sinx) #?

1 Answer
Nov 19, 2015

Use the Chain Rule to get #f'(x)=sec^{2}(sin(x)) * cos(x)#.

Explanation:

We know that #d/dx(tan(x))=sec^{2}(x)=1/(cos^{2}(x))# and #d/dx(sin(x))=cos(x)#. The Chain Rule can be written as #d/dx(g(h(x)))=g'(h(x)) * h'(x)#.

To apply the Chain Rule to #f(x)=tan(sin(x))#, let the "outside" function be #g(x)=tan(x)# and the "inside" function be #h(x)=sin(x)#.