1. gradient$$\nabla(r^n) = \nabla\left( (x^2 + y^2 + z^2)^{n/2} \right) $$$$ \text{x component: } \frac{d}{dx} \left( (x^2 + y^2 + z^2)^{n/2} \right) = \frac{n}{2} (x^2 + y^2 + z^2)^{\frac{n}{2}-1} \cdot 2x = n x (r^2)^{\frac{n}{2}-1} = n x r^{n-2} $$$$ \Rightarrow (n x r^{n-2}, n y r^{n-2}, n z r^{n-2}) = n r^{n-2} (x, y, z) $$$$ \Rightarrow \nabla(r^n) = n r^{n-2} \vec{r} = n r^{n-1} \hat{r..