Question

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

Answer 1

\[\huge \frac{dA}{dt}= \frac{dA}{dr}\frac{dr}{dt}\]

Answer 2

chain rule

Answer 3

\[\huge A=\pi r ^{2}\]
\[\huge \frac{dA}{dr}=2\pi r \]
When r=1
\[\huge \frac{dA}{dr}=2\pi \]

Answer 4

\[\huge \frac{dA}{dt}=2 \pi (3)=6\pi\]