Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 18


$$ y'= -e^{\coth x}csch^2 (x) .$$

Work Step by Step

Recall that $(\coth x)'=-\csc^2 x$ Recall that $(e^x)'=e^x$ Since $ y=e^{\coth x}$, then the derivative, by using the chain rule, is given by $$ y'=e^{\coth x} (\coth x)'= -e^{\coth x}csch^2 (x) .$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.