Partial derivatives of $g(x,y,z)=f(x-y,y-z,z-x)$. Let $f$ be two times differentiable function of variables $u,w,v$ and define $g(x,y,z)=f(x-y,y-z,z-x)$. Determine $\frac{\partial g}{\partial x}+\frac{\partial g}{\partial y}+\frac{\partial g}{\partial z}$ and express $\frac{\partial^2 g}{\partial x^2}$ in partial derivates of $f$.
This is from calc 3. I don't know how to solve this at all but I suspect there is some easy rule to do this. Help would be appreciated.

Hint:  Notice that we can use a tree diagram. Then with a change of variables $g(x,y,z)=f(u,v,w)$ and finally Chain rule.

