Having problems with how to obtain the following, I have written in my notes but can't see how the end result is formed.
Using spherical co-ordinates $(r, \theta, \phi)$ evaluate $\nabla \phi$ and show that $\nabla \wedge( \cos(\theta)\nabla\phi)=\nabla(1/r)$
Now ${\mathbf r} = x \mathbf{i}+y \mathbf{j}+z \mathbf{k}= r \sin(\theta) \cos(\phi) \mathbf{i} + r \sin(\theta) \sin(\phi) \mathbf{j} + r \cos(\theta) \mathbf{k}$
It says that $\nabla \phi$ = $\frac {1}{r\sin(\theta)} {\bf e_{\phi}}$
I'm just confused to how you get to this?
As for the $\nabla \wedge( \cos(\theta)\nabla\phi)=\nabla(1/r)$ this makes more sense to me, once the first part is obtained.
Many thanks in advance.