Answer
$\coth z$
Work Step by Step
Since, $\dfrac{d}{dx} (\sinh x)=cosh x$
As we are given that $y=\ln (\sinh z)$
Then, on differentiating , we have:
$\dfrac{dy}{dz}= (\cosh z) \dfrac{1}{\sinh z} =\coth z$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 17
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