Answer
$2\cot x$
Work Step by Step
$\frac{d}{dx}\ln(\sin^2 x)$
$=\frac{1}{\sin^2 x}*\frac{d}{dx}\sin^2 x$
$=\frac{1}{\sin^2 x}*2\sin x\frac{d}{dx}\sin x$
$=\frac{1}{\sin^2 x}*2\sin x\cos x$
$=\frac{2\cos x}{\sin x}$
$=2\cot x$
Calculus 8th Edition
by Stewart, James
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 - Page 436: 4
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