Question

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

Answer 1

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)`.