Proving the chain rule of a given function

Question

Suppose that $f'(2)=3$, $f'(5)=4$, and let $h(x)$ be the composite function $h(x) = f(x^2+1)$. Find $h'(2)$

I get how to prove the $f'g(x)*g'(x)$ part, which leads to $4*g'(2)$ but how do I prove $g'(2)$ with the information given? Or was I given $f'(2)=3$ to throw me off?

Answer 1

First notice that

$$ h'(x) = f'(x^2+1)2x $$

Now, set $x=2$ to get

$$ h'(2) = f'(2^2+1)4 = f'(5)4 $$

Finally, use the fact that $f'(5)=4$ to obtain

$$ h'(2) = 16.$$

Answer 2

I believe this is the answer: $$h(x)=f(x^2 +1)$$ $$\Rightarrow h'(x)=2xf'(x^2+1)\\ \Rightarrow h'(2)=4f'(5)=16$$ They give you $f'(2)$ in case you don't apply the chain rule correctly, like this: $$h'(x)=2xf'(x)$$ And the result would be 12, which is wrong!