Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Review - Exercises - Page 267: 13


$-\dfrac {e^{\frac {1}{x}}\left( 1+2x\right) }{x^{4}}$

Work Step by Step

$\dfrac {d}{dx}\left( \dfrac {e^{1/x}}{x^{2}}\right) =\dfrac {\dfrac {d}{dx}\left( e^{1/x}\right) {\times}x^{2}-\left( \dfrac {d}{dx}\left( x^{2}\right) \right) \times e^{1/x}}{x^{4}}=e^{1/x}\times x^{2}\times \dfrac {d}{dx}\left( \dfrac {1}{x}\right) -2x\times e^{\frac {1}{x}}=-\dfrac {e^{\frac {1}{x}}\left( 1+2x\right) }{x^{4}}$
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