Prove that $\displaystyle div \vec{e}=0$ if $\displaystyle e=\frac{\vec{r}}{r^3}$

1. $\displaystyle div\vec{e}=div\frac{\vec{r}}{r^3}$

2. $\displaystyle =(grad\frac{1}{r^3})\vec{r} + \frac{1}{r^3}div\vec{r}$

3. $\displaystyle =-3\vec{r}\frac{1}{r^4}grad{\vec{r}}+\frac{1}{r^3}3$

Here are the first three steps of the solution i have in the book, i know how to go after step three, here is what i can't figure out:

What is done in step 1 that leads to step 2?

Why is $\displaystyle div\vec{r}=3$?