Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises: 34

Answer

$$F'(t)=\coth t$$

Work Step by Step

$F'(t)=\frac{d}{dt}\ln{(\sinh t)}$ Using the chain rule: $F'(t)=\frac{d\ln{(\sinh t)}}{d\sinh t} \times \frac{d\sinh t}{dt}$ $=\frac{1}{\sinh t} \times \cosh t$ $=\frac{\cosh t}{\sinh t}$ $=\coth t$
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