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: 18



Work Step by Step

Using the product rule, we have $ f'(x)=\frac{d}{dx}(\frac{1}{x}-x^{2})\times(x^{3}+1)+(\frac{1}{x}-x^{2})\times\frac{d}{dx}(x^{3}+1)$ $=(-\frac{1}{x^{2}}-2x)(x^{3}+1)+(\frac{1}{x}-x^{2})3x^{2}$ $=(-x-\frac{1}{x^{2}}-2x^{4}-2x)+(3x-3x^{4})$ $=-5x^{4}-\frac{1}{x^{2}}$
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