In his book introduction to electrodynamics, Griffiths uses derives the identity $$\nabla \cdot \frac{\mathbf{\hat{r}}}{r^2} = 4\pi\delta^3(\mathbf{r})$$ Using the formula for divergence in polar coordinates. He then states that "more generally" $$\nabla \cdot \frac{\mathbf{\hat{r_s}}}{r_s^2} = 4\pi\delta^3(\mathbf{r_s})$$ Where $\mathbf{r_s}$ is the seperation vector, $\mathbf{r}-\mathbf{r'}$ and $\mathbf{r'}$ is a constant. I'm trying to find a way to derive this identity using polar coordinates, but am struggling to find a way to represent $\frac{\mathbf{r-r'}}{{|r-r'|^3}}$ in terms of the basis vectors in polar coordinates $(\mathbf{\hat{r}}, \hat{\boldsymbol{\phi}},\hat{\boldsymbol{\theta}})$ as $v_r\mathbf{\hat{r}}+v_\theta\boldsymbol{\hat{\theta}}+v_\phi\boldsymbol{\hat{\phi}}$ for some scalar functions $v_r, v_{\theta}, v_{\phi} $ to use in the formula for divergence in polar coordinates.