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 - Page 191: 35


a. $\frac{d}{dx}cos^3(x) =-3cos^2(x)sin(x)$ b. $\frac{d}{dx}cos(x^3) =-3x^2sin(x^3) $

Work Step by Step

Chain Rule: $\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$ a. $y=cos^3(x)$ Outer Function: $y=f(u)=u^3$ Inner Function: $u=g(x)=cos(x)$ $\frac{d}{dx}cos^3(x) = 3cos^2(x) \times -sin(x)$ b. $y=cos(x^3)$ Outer Function: $y=f(u)=cos(u)$ Inner Function: $u=g(x)=x^3$ $\frac{d}{dx}cos(x^3) = -sin(x^3) \times 3x^2$
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