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: 51


$y’=\frac{x}{(x^2-1)(\ln 5)}$

Work Step by Step

$y=\frac{(\frac{1}{2})\ln(x^2-1)}{\ln 5}$ $u=\frac{1}{2} \ln(x^2-1)$ $u’=\frac{x}{x^2-1}$ $v=\ln 5$ $v’=0$ $y’=\frac{u’v-uv’}{v^2}$ $=\frac{\left(\frac{x}{x^2-1}\right)(\ln 5)-(\frac{1}{2} \ln(x^2-1))(0)}{(\ln 5)^2}$ $y’=\frac{x}{(x^2-1)(\ln 5)}$
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