The question is:
Suppose $w=xy^2 +4x^2 - 5y$, and $x=g(t)$ and $y=h(t)$, where $g(0)=6$, $g'(0)=4$, $h(0)=-4$, and $h'(0)=-3$. Find $\frac{dw}{dt}$ at $t=0$.
What I have done is: $$w = g'(t) h(t)^2 + 2 h'(t) g(t) + 8 g(t) - 5 h'(t)$$ and then I substituted in the values as provided by the question and I received 91 which is incorrect.
I appreciate any help, thank you.
Hint
$$\frac{d}{dt} f(t)^2=2f(t)f'(t).$$
So, you need to check
$$w'(t) = g'(t) h(t)^2 + \color{red}{2 h'(t) g(t)} + \color{red}{8 g(t)} - 5 h'(t)$$