Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Review - Exercises: 29

Answer

$\dfrac {\cos ^{3}x}{\sin x}$ or $\cot{x}-\sin{x}\cos{x}$

Work Step by Step

$\dfrac {d}{dx}\left( \ln \sin x-\dfrac {1}{2}\sin ^{2}x\right) =\dfrac {1}{\sin x}\times \left( \dfrac {d}{dx}\sin x\right) -\sin x\times \left( \dfrac {d}{dx}\sin x\right) =\cos x\left( \dfrac {1}{\sin x}-\sin x\right) =\dfrac {\cos ^{3}x}{\sin x}$
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