Find h'(1)?

Question

Let f and g be differentiable functions such that f(1)=2, g(1)=2, f'(1)=3, g'(1)=-3, f'(2)=-4, g'(2)=5. If h(x)=f(g(x)), find h'(1).

 

Answer: 12

Answer 1

h’(x) = f’(g(x)) * g’(x) by chain rule
h’(1) = f’(g(1)) * g’(1)
= f’(2) * (-3)
= (-4) * (-3)
= 12