Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.7 The Chain Rule - 3.7 Exercises: 1

Answer

Where $y=f(x)$ and $u=g(x)$, the two ways to write the derivative of $y=f(g(x))$ is: 1. $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ 2. $\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$

Work Step by Step

According to Theorem 3.14, where $y=f(x)$ and $u=g(x)$, the two ways to write the derivative of $y=f(g(x))$ is: 1. $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ 2. $\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$
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