Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 362: 63


$y'=(2x^{\frac{2}{x}-2}(1-\ln x))$

Work Step by Step

$y=x^{\frac{2}{x}}$ $y’=(x^{\frac{2}{x}})(\frac{d}{dx} \ln x (\frac{2}{x}))$ $u= 2\ln x$ $u’= \frac{2}{x}$ $v=x$ $v’=1$ $y’=(\frac{(\frac{2}{x})(x)-(2 \ln x)(1)}{x^2})(x^{\frac{2}{x}})$ $=(2x^{\frac{2}{x}-2}(1-\ln x))$
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