Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 374: 38


$$ y'= -\frac{e^{\cos^{-1}x}}{\sqrt{1-x^2}}.$$

Work Step by Step

Since $ y=e^{\cos^{-1}x}$, then the derivative $ y'$ is given by $$ y'=e^{\cos^{-1}x} (\cos^{-1}x)'=e^{\cos^{-1}x} \left(-\frac{1}{\sqrt{1-x^2}}\right)=-\frac{e^{\cos^{-1}x}}{\sqrt{1-x^2}}.$$
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