Answer
$\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$
Work Step by Step
Area of a circle (A) is determine by equation $\pi r^2$
so A = $\pi r^2$
on differentiation of area with respect to time, we get:
$\frac{dA}{dt}$ = $\frac{d\pi r^2}{dt}$
we obtain: $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$
the final answer is: $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$