Area of a circle

Question

Let A be the area of a circle with radius r. If dr/dt= 3 , find dA/dt when r = 1.

Answer 1

r'=3

r = 1

A= pi(r^2) = area of a circle with radius = r

take the derivative

A' = 2pi(r)(r') = 2pi(1)(3) = 6pi

Answer 2

A = πr²; dA/dt = 2πrdr/dt = 2π·1·3 = 6π