How do you find the first order partial derivatives of a function that contains another derivable function?

Question

As the title says, I have a function which contains another derivable function and I need to find the first order partial derivatives of the bigger function. Can anyone guide me through this?

Ex: $ F(x,y)=x^2 * y * h(x^2+y^2)$, where $h$ is a derivable function.

Answer 1

You mean "differentiable", I believe. Use the product and chain rules $$ \frac{\partial F}{\partial x}=2xyh(x^2+y^2)+2x^3yh'(x^2+y^2) $$ and similarly for $\frac{\partial F}{\partial y}$.