Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.4 Rates of Change - Exercises - Page 130: 19


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