University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 47



Work Step by Step

$y=\log_{2}{(\frac{x^2}{2})}=\frac{\ln\frac{x^2}{2}}{ln2}$ On differentiating both sides: $\frac{dy}{dx}=\frac{1}{ln{2}}\frac{d(\ln\frac{x^2}{2})}{dx}$ $\frac{dy}{dx}=\frac{1}{\ln{2}}\frac{1}{\frac{x^2}{2}}\frac{d(\frac{x^2}{2})} {dx}$ $\frac{dy}{dx}=\frac{1}{\ln{2}}\frac{2}{x}$
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