how to tackle this partial differentiation problem

Question

show that if $$f(x, y, z)=0$$ then $$\left ( \partial x \over \partial y \right )_{z}\left ( \partial y \over \partial z \right )_{x}\left ( \partial z \over \partial x \right )_{y}=-1$$

I don't know how to tackle this problem although I've tried.

Answer 1

I could write it all out, but I think that what you are referring about is the triple product rule. A derivation can be found on:

https://en.wikipedia.org/wiki/Triple_product_rule