University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.3 - Differentiation Rules - Exercises: 15

Answer

$y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$

Work Step by Step

Using product rule: $y = (x^{2}+1)(x+5+\frac{1}{x})$ $y'= (x^{2}+1)(1-\frac{1}{x^{2}}) + (x+5+\frac{1}{x})(2x)$ $y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$ Using sum of simpler terms: $y = x^{3} +5x^{2} + 2x + \frac{1}{x} +5$ $y' = 3x^{2}+10x+2-\frac{1}{x^{2}}$ $y ' = 3x^{2}- \frac{1}{x^{2}} +10x +2$
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