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: 25



Work Step by Step

Using quotient rule, we have $\frac{d}{dx}(\frac{1}{x^{3}+1})=\frac{(x^{3}+1)\times\frac{d}{dx}(1)-1\times\frac{d}{dx}(x^{3}+1)}{(x^{3}+1)^{2}}$ $=\frac{-3x^{2}}{(x^{3}+1)^{2}}$ $\frac{dz}{dx}|_{x=1}=\frac{-3(1)^{2}}{((1)^{3}+1)^{2}}=-\frac{3}{4}$
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