If f is a differentiable function, find an expression for the derivative of each of the following functions:

a) g(x)= f(x^2)

This one I am having trouble with. I applied chain rule to solve, which gave me g'(x)= f'(x^2)*(2x), but the answer in the book says its supposed to be f(x^2)*(2x). What am I doing wrong?

b) h(x)= 2xf(x)

I answered this using product rule,

h'(x)= (2)f(x)+(2x)f'(x)