Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.7 Hyperbolic Functions - 6.7 Exercises - Page 490: 34


$\coth t$

Work Step by Step

Given: $F(t)=\ln{(\sinh t)}$ Now, $F'(t)=\dfrac{d}{dt}[\ln{(\sinh t)}]$ On applying the chain rule, we have $F'(t)=(\dfrac{d\ln{(\sinh t)}}{d\sinh t})(\dfrac{d\sinh t}{dt})$ or, $=(\dfrac{1}{\sinh t})(\cosh t)$ or, $=\dfrac{\cosh t}{\sinh t}$ $=\coth t$
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