How do you find the derivative of #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