Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises: 22

Answer

$$y'=5(x+\frac{1}{x})^4(1-\frac{1}{x^2})$$

Work Step by Step

$$y'=((x+\frac{1}{x})^5)'=5(x+\frac{1}{x})^{4}\cdot(x+\frac{1}{x})'= 5(x+\frac{1}{x})^4(1+(-\frac{1}{x^2})=5(x+\frac{1}{x})^4(1-\frac{1}{x^2})$$
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