Answer
$v'_{esc} = -1.41$ x $10^7r^{-3/2}\ m/s$
Work Step by Step
$v_{esc} = (2.82$ x $10^7)r^{-1/2}$
To find the rate of change, we need to find the derivative, which can be done using the power rule:
$v'_{esc} = (2.82$ x $10^7)(-\frac{1}{2})r^{-3/2}$
$v'_{esc} = -1.41$ x $10^7r^{-3/2}\ m/s$
