Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises: 8

Answer

$G'(x)=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$

Work Step by Step

$G(x)=\dfrac{x^{2}-2}{2x+1}$ Differentiate using the quotient rule $G'(x)=\dfrac{(2x+1)(x^{2}-2)'-(x^{2}-2)(2x+1)'}{(2x+1)^{2}}=\dfrac{(2x+1)(2x)-(x^{2}-2)(2)}{(2x+1)^{2}}=...$ Evaluate the product in the numerator $...=\dfrac{4x^{2}+2x-2x^{2}+4}{(2x+1)^{2}}=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$ $G'(x)=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$
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