Starting from Coulomb's law, derive Gauss's law in differential form.
Coulomb’s law states that the electric field due to a point charge (q) located at the origin is [ \mathbf{E}=\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}\hat{\mathbf{r}} ] where (r) is the distance from the charge and (\hat{\mathbf{r}}) is the radial ________ ____ _____ ___ ______ __________ ________ _________ _______ _______ _________ ________.
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Starting from Coulomb's law, derive Gauss's law in differential form.