设 $r=\sqrt{x^2+y^2+z^2}$, 证明: $\frac{\partial^2(\ln r)}{\partial x^2}+\frac{\partial^2(\ln r)}{\partial y^2}+\frac{\partial^2(\ln r)}{\partial z^2}=\frac{1}{r^2}$.
设 $r=\sqrt{x^2+y^2+z^2}$, 证明: $\frac{\partial^2(\ln r)}{\partial x^2}+\frac{\partial^2(\ln r)}{\partial y^2}+\frac{\partial^2(\ln r)}{\partial z^2}=\frac{1}{r^2}$. 即 $\Delta(\ln r)=\frac{1}{r^2}$.