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: 25


$$ y'= \frac{3}{\sqrt{(3x)^2-1}} . $$

Work Step by Step

Recall that $(\cosh^{-1} x)'=\dfrac{1}{\sqrt{x^2-1}}$ Since $ y= \cosh^{-1} (3x)$, then the derivative, by using the chain rule, is given by $$ y'= \frac{1}{\sqrt{(3x)^2-1}} (3x)'=\frac{3}{\sqrt{(3x)^2-1}} .$$
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