Answer
$-\left( x-1\right) ^{-2}$
Work Step by Step
$\dfrac {d}{dx}\left( 1-x^{-1}\right) ^{-1}=-\left( 1-x^{-1}\right) ^{-2}\times \dfrac {d}{dx}\left( -x^{-1}\right) =-\left( 1-x^{-1}\right) ^{-2}\times x^{-2}=-\left( x-1\right) ^{-2}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 3 - Review - Exercises - Page 267: 23
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