University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.6 - The Chain Rule - Exercises - Page 158: 4


$\frac{dy}{dx} = e^{-x}sin u=e^{-x}sin(e^{-x})$

Work Step by Step

$\frac{dy}{du} = \frac{d(cos u)}{du} = -sin u$ and, $\frac{du}{dx} = \frac{d(e^{-x})}{dx} = -e^{-x}$ So, $\frac{dy}{dx} = \frac{dy}{du}*\frac{du}{dx} $ $\frac{dy}{dx} = e^{-x}sin u$
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