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
$$ y'=(1-x)^{-2}$$
$$ y''=2(1-x)^{-3}, \quad y'''=6(1-x)^{-4}$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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