Answer
$\frac{dA}{dr}$= 6$\pi$
Work Step by Step
A=$\pi$$r^{2}$
Differentiate with respect to radius to find rate of change of each variable:
$\frac{d}{dr}$(A=$\pi$$r^{2})$=
$\frac{dA}{dr}$=2*($\pi$$r^{2-1}$)*$\frac{dr}{dr}$
Plug in known values (r=3, $\frac{dr}{dr}$=1)
$\frac{dA}{dr}$=2$\pi$(3)(1)= 6$\pi$