Answer
$f'(x) = \frac{1-x}{e^x}$
Work Step by Step
$f(x)=xe^{-x} = \frac{x}{e^x}$
Quotient Rule:
$f'(x) = \frac{(1)(e^x)-(x)(e^x)}{e^{2x}} = \frac{e^x-xe^x}{e^{2x}} = \frac{1-x}{e^x}$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 3 - Derivatives - 3.4 The Product and Quotient Rules - 3.4 Exercises - Page 160: 23
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