Gradient function?

[Pseudo Statistic]

I was reading this ebook when I found Coulomb's law:
http://www.brokendream.net/xh4/elec.jpg
What I'm unsure of is how the gradient function applied to 1/|x-x'| is the same thing as |x-x'|/|x-x'|^3...
I know what the gradient function is but I'm totally lost as to how the formula was transformed that way..
Can anyone care to explain?
Thanks alot.

[dextercioby]

Compute

\nabla_{\vec{r}}\left(\frac{1}{r}\right)

,for

r=:\sqrt{(x-x')^{2}+(y-y')^{2}+(z-z')^{2}}

and

\nabla_{\vec{r}}=\frac{\partial}{\partial x} \vec{i}+ \frac{\partial}{\partial y} \vec{j} +\frac{\partial}{\partial z} \vec{k}

Daniel.