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

Answer 1

This is an example of using chain rule (or related rates) where t is your independent variable.

dA/dt = π(2r)(dr/dt)

because π is just a constant,

the derivative or r² is 2r, but since r DEPENDs on t, you need to multiply by the derivative of r with respect to t.