Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - Review - Exercises: 22

Answer

$-\dfrac {\left( 1-\cos x\right) \left( \cos \left( x-\sin x\right) \right) }{\sin ^{2}\left( x-\sin x\right) }$

Work Step by Step

$y=\dfrac {1}{\sin \left( x-\sin x\right) }\Rightarrow y'=-\dfrac {\left( \cos \left( x-\sin x\right) \right) \times \left( \dfrac {d}{dx}\left( x-\sin x\right) \right) }{\sin ^{2}\left( x-\sin x\right) }=-\dfrac {\left( 1-\cos x\right) \left( \cos \left( x-\sin x\right) \right) }{\sin ^{2}\left( x-\sin x\right) }$
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