Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 14

Answer

$$ y''=2(1-x)^{-3}, \quad y'''=6(1-x)^{-4}$$

Work Step by Step

Let $ y=\frac{1}{1-x}$; rewrite $ y $ as follows $$ y=(1-x)^{-1}.$$ Now, we get $$ y'=(1-x)^{-2}$$ $$ y''=2(1-x)^{-3}, \quad y'''=6(1-x)^{-4}$$
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