If $\displaystyle u=\frac{xy}{z}lnx+xf(\frac{y}{x},\frac{z}{x})$ and $\displaystyle f$ is differentiable at least once, prove that:

$\displaystyle x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}+z\frac{\partial u}{\partial z}=u+\frac{xy}{z}$

How to find the partial derivative with respect of x,y,z of that function f when it's not expressed.

Thanks