How to find the resultant derivative when I know the outputs of $f_{x}$ and $f_{y}$? I have this problem:
Find $h'(1)$ where $h(t)=f(t^{2}-4t,5-4t^{3})$, $f$ is a differentiable function and $f_{x}(-3,1)=2$ and $f_{y}(-3,1)=6$.
My first thought was how do I find the resultant derivative of the differentiable $f$.
Some tips, or ideas to solve this...

This is nothing but an application of chain rule:
Let $x(t)=t^2-4t, y(t)=5-4t^3$. Then $h(t)=f(x(t),y(t))$. 
So $\displaystyle \frac{dh}{dt}=\frac{d(f(x(t),y(t)))}{dt}=\frac{\partial(f(x(t),y(t)))}{\partial x}\frac{dx}{dt}+\frac{\partial(f(x(t),y(t)))}{\partial y}\frac{dy}{dt}$. 
Now plug in $t=1$. That will give you the answer.
