要点1（红色标注）：多元复合函数求偏导的链式法则。总则：$\frac{\partial(\text{函数})}{\partial(\text{自})} = \sum_{\text{中}} \frac{\partial(\text{函数})}{\partial(\text{中})} \cdot \frac{\partial(\text{中})}{\partial(\text{自})}$。对于 $z=f(u,v)$，$u=\varphi(x,y)$，$v=\psi(x,y)$，有 $\frac{\partial z}{\partial x} = \frac{\partial f}{\partial u}\frac{\partial u}{\partial x} + \frac{\partial f}{\partial v}\frac{\partial v}{\partial x}$，$\frac{\partial z}{\partial y} = \frac{\partial f}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial f}{\partial v}\frac{\partial v}{\partial y}$。要点2（红色标注）：抽象复合函数求偏导的简便记法——$f(u,v)$，记 $f_u=f_1'$，$f_v=f_2'$，$f_{uv}=f_{12}''$ 等。注意：若 $f(u,v)$ 是 $u,v$ 的函数，则 $f_1'$ 和 $f_2'$ 仍然保持与 $f$ 相同的复合结构。