Thomas' Calculus 13th Edition

$\dfrac{dA}{dt} = 2\pi r \dfrac{dr}{dt}$
Area of a circle, A can be determined as:$\pi r^2$, Thus, A = $\pi r^2$ On differentiation , we get: $\dfrac{dA}{dt}$ = $\dfrac{d\pi r^2}{dt}$ or, $\dfrac{dA}{dt} = 2\pi r \dfrac{dr}{dt}$ Hence, $\dfrac{dA}{dt} = 2\pi r \dfrac{dr}{dt}$