关于一个表达式的笛卡尔分解问题
-
$$
\begin{aligned}
\nabla(\nabla \cdot \nabla) f
&=
\nabla \left(\frac{\partial^{2} f}{\partial {x}^{2}}+\frac{\partial^{2} f}{\partial {y}^{2}}+\frac{\partial^{2} f}{\partial {z}^{2}}\right)\
&=\frac{\partial}{\partial x}\left(\frac{\partial^{2} f}{\partial {x}^{2}}+\frac{\partial^{2} f}{\partial {y}^{2}}+\frac{\partial^{2} f}{\partial {z}^{2}}\right) \vec i+\frac{\partial}{\partial y}\left(\frac{\partial^{2} f}{\partial {x}^{2}}+\frac{\partial^{2} f}{\partial {y}^{2}}+\frac{\partial^{2} f}{\partial {z}^{2}}\right) \vec j+\frac{\partial}{\partial z}\left(\frac{\partial^{2} f}{\partial {x}^{2}}+\frac{\partial^{2} f}{\partial {y}^{2}}+\frac{\partial^{2} f}{\partial {z}^{2}}\right) \vec k
\end{aligned}
$$
