Does a Function f(x,y,z) Satisfy Given Partial Derivatives?

[kokai]

$f(x,y,z)$ is function that:
$x^{q-1}\frac{\partial f}{\partial x}=<br /> y^{q-1}\frac{\partial f}{\partial y}=<br /> z^{q-1}\frac{\partial f}{\partial z}$.

How to prove that exists function $g$:
$f(x,y,z)=g(x^q+y^q+z^q)$

 

[Simon Bridge]

Have you tried doing the differentiation?