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: 37


$y'=3e^{\cosh 3x}\sinh (3x)$

Work Step by Step

Given: $y=e^{\cosh 3x}$ Now, $y'=\dfrac{d}{dx}[e^{\cosh 3x}]$ Apply chain rule. $y'=(\dfrac{de^{\cosh 3x}}{d\cosh 3x})(\dfrac{d\cosh 3x}{d3x}) (\dfrac{d(3x)}{dx})$ or, $=e^{\cosh 3x}(\sinh 3x)(3)$ Thus $y'=3e^{\cosh 3x}\sinh (3x) $
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