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 - Page 265: 38


$$f'(t)=\frac{2\cosh t}{(1-\sinh t)^2}$$

Work Step by Step

$f'(t)=\frac{d}{dt}\frac{1+\sinh t}{1-\sinh t}$ Using the quotient rule: $f'(t)=\frac{\cosh t(1-\sinh t)-(1+\sinh t)(-\cosh t)}{(1-\sinh t)^2}$ $=\frac{\cosh t-\cosh t\sinh t+\cosh t+\cosh t\sinh t}{(1-\sinh t)^2}$ $=\frac{2\cosh t}{(1-\sinh t)^2}$
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