If $h(x) = f((g(x))^2)$, find $h'(x)$ using the following values:
$$f(2) = 4$$ $$f(4) = -5$$ $$f'(2) = -2$$ $$f'(4) = 7$$ $$g(2) = 2$$ $$g(4) = 4$$ $$g'(2) = 3$$ $$g'(4) = 8$$
This is what I have : $f((g(x))^2) \cdot (g'(x))^2$. When I try to plug in the values, I get $f(16)$, which is not given. Thank you in advance!
This is actually a composition of three function, so you need to apply the chain rule twice.
$$h'(x) = f'(g(x)^2) \cdot (g(x)^2)' = f'(g(x)^2) \cdot 2g(x) \cdot g'(x)$$