Use the chain rule
$\displaystyle \frac{\partial f}{\partial u} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial u}+\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}$
$\displaystyle \frac{\partial f}{\partial u}=(3x^2-2xy)(1)+(-x^2-2z^2y)(1)+(-2zy^2)(0)$
From here just sub in