if $\displaystyle f(x,y,z)=0$ then,

$\displaystyle (\frac{\partial x}{\partial y})_z (\frac{\partial y}{\partial z})_x (\frac{\partial z}{\partial x})_y = -1 $

I tried expressing $\displaystyle \frac{\partial f}{\partial x}$ with z constant but this didnt work

Im lost. Help much appreciated