A spherical balloon is expanding with time where r = 3t. What is the formula for the rate of change of the volume of the balloon with respect to time?
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V = 4/3 π r³
Differentiate both sides with respect to t (using chain rule on right)
d/dt (V) = 4/3 π d/dt (r³)
dV/dt = 4/3 π * 3r² dr/dt
dV/dt = 4π r² dr/dt
Differentiate both sides with respect to t (using chain rule on right)
d/dt (V) = 4/3 π d/dt (r³)
dV/dt = 4/3 π * 3r² dr/dt
dV/dt = 4π r² dr/dt