Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 24



Work Step by Step

Using the quotient rule, we have $f'(x)=\frac{(x+1)\frac{d}{dx}(x^{4}+x^{-1})-(x^{4}+x^{-1})\frac{d}{dx}(x+1)}{(x+1)^{2}}$ $=\frac{(x+1)(4x^{3}-\frac{1}{x^{2}})-(x^{4}+x^{-1})\times1}{(x+1)^{2}}$ $=\frac{3x^{4}+4x^{3}-2x^{-1}-x^{-2}}{(x+1)^{2}}$
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