find curl and div of $\vec{A} = \vec{r}\mathrm{sh}(\vec{a} \cdot \vec{r})$

Question

Actually the task is easy, I more about calculus way, than about the task itself. The vector function is:

$$\vec{A} = \vec{r}\mathrm{sh}(\vec{a} \cdot \vec{r})$$

And I have to find curl and div for it

I rewrote it like:

$$\vec{A} = (x,y,z)\mathrm{sh}(xa_x,ya_y,za_z)$$

Am I right about it, or is there easier way, how should I proceed?

And how should I apply derivatives rules here, like this? $$((x,y,z))' \cdot (\mathrm{sh}(xa_x,ya_y,za_z))'$$

for $x$, $y$ and $z$

Answer 1

You are right. This is the easiest way. Now apply the definitions of curl to find the result.