Gradient, divergence and curl - nabla dotted with f(r)r

Sorry for the naff title, couldn't think of anything else. I've ended with a ridiculous answer...

**a)** Find $\displaystyle \nabla\cdot\left(f(r)\mathbf{r}\right)$, where $\displaystyle r=|\mathbf{r}|$, $\displaystyle \mathbf{r}=(x,y,z)$ and $\displaystyle f$ is a differentiable function.

**b) **In Part (a), find $\displaystyle f(r)$ such that $\displaystyle \nabla\cdot\left(f(r)\mathbf{r}\right)=0$.

I ended up with something like $\displaystyle \frac{df}{dr}r+3f(r)$ for part a), which I highly doubt is right (Worried) thus I can't really attempt part b)... cheers in advance.