已知 $z=f(u, v, w)$ 具有连续偏导数，而 $u=\eta-\zeta, v=\zeta-\xi, w=\xi-\eta$ ，求 $\frac{\partial z}{\partial \xi}, \frac{\partial z}{\partial \eta}, \frac{\partial z}{\partial \zeta}$ ，

$$
\frac{\partial^2 z}{\partial \xi \partial \eta}, \frac{\partial^2 z}{\partial \zeta^2}
$$