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

2 Answers
Apr 13, 2015

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)

Apr 13, 2015

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