University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 20


$\text{csch} \theta \text{coth} \theta (\ln csch \theta)$

Work Step by Step

Since, $\dfrac{d}{dx} (csch x)=\text{-csch} x \text{coth} x$ As we are given that $y=csch \theta (1-\ln csch \theta)$ Then, on differentiating , we have: $\dfrac{dy}{d \theta}=csch \theta[\dfrac{-1}{csch \theta}( -csch \theta coth \theta)]+(1-\ln csch \theta)=(csch \theta coth \theta)[1-(1-\ln csch \theta)]=\text{csch} \theta \text{coth} \theta (\ln csch \theta)$
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