Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 6



Work Step by Step

Let $ g(x)=u= x^{3}$ and $ f(u)=y=\cos u $ Then, $ y=f(g(x))=\cos(x^{3})$ Using the chain rule, we have $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}=-\sin (u)\times3x^{2}=-3x^{2}\sin(x^{3})$
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