Answer
$$F'(t)=\coth t$$
Work Step by Step
$F'(t)=\frac{d}{dt}\ln{(\sinh t)}$
Using the chain rule:
$F'(t)=\frac{d\ln{(\sinh t)}}{d\sinh t}
\times \frac{d\sinh t}{dt}$
$=\frac{1}{\sinh t} \times \cosh t$
$=\frac{\cosh t}{\sinh t}$
$=\coth t$
Calculus: Early Transcendentals 9th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1337613924
ISBN 13:
978-1-33761-392-7
Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises - Page 267: 40
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