Question

How do you find the derivative of `f(x) = tan(sinx)`?

Answer 1

`f'(x)=(cosx)sec^2(sinx)`

`f(x)=tan(sinx)`

Differentiating both side with respect to 'x'

`f'(x)=sec^2(sinx)d/(dx)(sinx)`

`f'(x)=sec^2(sinx)(cosx)`

`f'(x)=(cosx)sec^2(sinx)`

Answer 2

`sec^2 (sin x)` cosx

Chain rule would would apply here. First differentiate tan with respect to sin x ( that would be `sec^2 (sinx)` and then differentiate sin x with respect to x(that would be cos x). It straight away leads to the result `sec^2 (sin x)` cos x