Question

If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2).

I am having problems with g'(2).

Answer 1

By the chain rule,


`g(x)=f(x^2)\implies g'(x)=2xf'(x^2)`

so


`g'(2)=2*2* f'(2^2)=4f'(4)`

You were able to find
`h'(2)=f'(f(2))* f'(2)`, which requires knowing both
`f(2)` and
`f'(2)`. Do you also happen to know
`f(4)` and
`f'(4)`?