Spherical coordinates vector question

[renlok]

I've no idea where to put this question but here it is I am trying to work through the examples our lecture has given in class and I wasn't getting them at all
the first thing that confused me was $\nabla . \underline{r} = 3$ I tried this myself with $\nabla . \underline{r} = \frac{1}{r^2}\frac{\delta{r^2}}{\delta{r}} = \frac{2}{r}$ (working in spherical coords)
but if you use $\textbf{e_r} = \frac{\textbf{r}}{r}$ it works but I have no idea where this comes from could someone at least point me in the right direction that would be really helpful thanks

 

[BruceW]

You should try to use the template. But oh well.

You've had a go at using spherical coordinates - yep that's one way to do it. But I think you've done it wrong. When the function is purely radial (as it is in your case), the divergence is equal to:

$$\frac{1}{r^2} \frac{\partial}{\partial r} (r^2 F)$$
(where F is the magnitude of the vector function in question). For your problem, F=r.