Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 141: 46

Answer

$\frac{-x^2-1}{(x^2-1)^2}$

Work Step by Step

Using the quotient rule: ($\frac{f}{g}$)^1: $\frac{g*f^1-g^1*f}{g^2}$ f(x)=$\frac{x}{x^{2}-1}$ f=x $f^1$=1 g=$x^2-1$ $g^1$=2x Now plug numbers into the quotinet rule formula: $\frac{(x^2-1)(1)-(2x)(x)}{(x^2-1)^2}$ simplify.... $\frac{x^2-1-2x^2}{(x^2-1)^2}$ simplify more... $\frac{-x^2-1}{(x^2-1)^2}$
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