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: 21

Answer

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

Work Step by Step

Derive the expression using the chain rule: $y=(x+\frac{1}{x})^5$ Apply the chain rule: $f(g(x)) = f'(g(x))g'(x)$: Set $g(x)$ equal to $u$ $g(x) = u = x + \frac{1}{x}$ $g'(x) = u' = 1 - \frac{1}{x^2}$ $y(u) = (u)^5 u'$ $y'(u) = 5(u)^4u'$ $y' = 5(x + \frac{1}{x})^4 ( 1 - \frac{1}{x^2})$
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