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: 21

Answer

$\frac{dy}{dx} = -7e^{5-7x}$

Work Step by Step

$y = e^{u}$ where, $u = 5-7x$ Now, $\frac{dy}{du} = e^{u} $ and, $\frac{du}{dx} = -7$ So, $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ $\frac{dy}{dx} = -7 \times e^{u}$ $\frac{dy}{dx} = -7e^{5-7x}$
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