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: 25


$\dfrac{1}{2 \sqrt{x(1+x)}} $

Work Step by Step

As we are given that $y=\sinh^{-1} \sqrt x$ Recall the formula: $\dfrac{d (\sinh^{-1} x)}{dx}=\dfrac{1}{\sqrt{1+x^2}}$ We need to use the chain rule to get the differentiation: Thus, $\dfrac{dy}{dx}=\dfrac{1}{\sqrt{1+(\sqrt x)^2}} (\dfrac{1}{2 \sqrt x})=\dfrac{1}{2 \sqrt{x(1+x)}} $
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