Example

Calculate the gradient of the distance $r=\vert\underline{r}\vert=\sqrt{x^2 + y^2 + z^2}$ of the point $(x,y,z)$ from the origin of the coordinates. Use of (A.4) yields :

$$\nabla r = \hat{x} \frac{\partial r}{\partial x} + \hat{y} \frac{... ...rac{x}{r}+\hat{y}\frac{y}{r}+\hat{z}\frac{z}{r}=\frac{\underline{r}}{r}=\hat{r}$$ (2.5)

where $\hat{r}$ is the unit vector directed from the origin of coordinates to the point $(x,y,z)$. Similarly:

$$\nabla r^2 = \nabla \left( x^2 + y^2 + z^2 \right) = 2\underline{r} \space .$$ (2.6)