Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 4

Answer

$2\cot x$

Work Step by Step

$\frac{d}{dx}\ln(\sin^2 x)$ $=\frac{1}{\sin^2 x}*\frac{d}{dx}\sin^2 x$ $=\frac{1}{\sin^2 x}*2\sin x\frac{d}{dx}\sin x$ $=\frac{1}{\sin^2 x}*2\sin x\cos x$ $=\frac{2\cos x}{\sin x}$ $=2\cot x$
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