Calculus: Early Transcendentals (2nd Edition)

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: 24


$\frac{1-2x}{2\sqrt x \times e^x}$

Work Step by Step

$(\frac{f}{g})'$ = $\frac{f'g-fg'}{g^2}$ $e^{-x}\sqrt x$ = $\frac{\sqrt x}{e^x}$ $(\frac{\sqrt x}{e^x})'$ = $\frac{(\frac{1}{2\times\sqrt x})(e^x)-(\sqrt x)(e^x)}{(e^x)^2}$ = $\frac{e^x-(e^x)(2x)}{2\sqrt x \times e^{2x}}$ = $\frac{1-2x}{2\sqrt x \times e^x}$
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