If h(x)=f(g(x))*g(x), then h'(1/2)= ?

Question

If h(x)=f(g(x))*g(x), then h'(1/2)= ? Calculus, no calculator question.

Answer 1

By the Chain Rule, the derivative of f(g(x) is 

f'(g(x))g'(x).

 

So, by the Product Rule, 

 

h'(x) = [f'(g(x))g'(x)]g(x) + f(g(x))[g'(x)]

 

To get a numerical value for h'(1/2), we would need to know the values of:  g(1/2), g'(1/2), f(g(1/2)), and f'(g(1/2)).