The Chain Rule & Implicit Differentiation · Medium problem

Let $f(u, v, w)$ be any differentiable function of three variables, and let $W(x,y,z) = f(x - y,\ y - z,\ z - x)$. Find the value of $\dfrac{\partial W}{\partial x} + \dfrac{\partial W}{\partial y} + \dfrac{\partial W}{\partial z}$.