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

[kokai]

f(x,y,z) is function that:
<br /> 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}<br />.

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?