Question

If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dx/dt

Answer 1

The area of a circle in terms of the circle's radius $r$ is

$A=\pi r^2$

Differentiating both sides with respect to $t$, you get

$\dfrac{\mathrm dA}{\mathrm dt}=2\pi r\dfrac{\mathrm dr}{\mathrm dt}$