Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 223: 19



Work Step by Step

$y=\ln \left(e^{-x}+x e^{-x}\right)\\ y^{\prime}=\frac{1}{e^{-x}+x e^{-x}} \times\left(-\frac{1}{e^{x}}+(x)\left(-e^{-x}\right)+\left(e^{-x}\right)(1))\right.\\ y^{\prime}=\frac{1}{e^{-x}+x e^{-x}} \times\left(\frac{-1-x+1}{e^{x}}\right)\\ y^{\prime}=-\frac{x}{1+x}$
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