If someone can help, please do help me for this question. I got stuck with it since yesterdays.

Prove that if f is a differentiable function of 3 variables and g(x,y,z) = f(x-y, y-z, z-x), then gsubx(x,y,z) + gsuby(x,y,z) +gsubz(x,y,z)=0.

Hint Let u =x-y, v=y-z, w=z-x, and write g(x,y,z)=f(u(x,y,z), v(x,y,z), w(x,y,z))

Thank you very much.