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: 16

Answer

$y' = \frac{3}{4}x^{-\frac{1}{4}} + 3x^{-4} + \frac{11}{4}x^{\frac{7}{4}}+x^{-2}$

Work Step by Step

Using product rule: $y = (1+x^{2})(x^{\frac{3}{4}} - x^{-3})$ $y' = (1 + x^{2})(\frac{3}{4}x^{-\frac{1}{4}}+3x^{-4}) + (x^{\frac{3}{4}} - x^{-3})(2x)$ $y' = \frac{3}{4}x^{-\frac{1}{4}} + 3x^{-4} + \frac{11}{4}x^{\frac{7}{4}}+x^{-2}$ Using sum of simpler terms: $y = x^{\frac{3}{4}} - x^{-3} + x^{\frac{11}{4}} - x^{-1}$ $y' = \frac{3}{4}x^{-\frac{1}{4}} + 3x^{-4} + \frac{11}{4}x^{\frac{7}{4}}+x^{-2}$
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