Calculus (3rd Edition)

$v'_{esc} = -1.41$ x $10^7r^{-3/2}\ m/s$
$v_{esc} = (2.82$ 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 $10^7r^{-3/2}\ m/s$