Calculate $\displaystyle x(\frac{\partial z}{\partial x})-y(\frac{\partial z}{\partial y})$ for $\displaystyle z=f(xy)$ where f is some differentiable function.

I am not sure if I am doing it right. This is what I have tried so far.

$\displaystyle \frac{\partial z}{\partial x} = \frac{\partial f}{\partial x}(y)$

$\displaystyle \frac{\partial z}{\partial y} = \frac{\partial f}{\partial y}(x)$

Help please..