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: 47


$y’=\frac{5}{(ln 4)(5x+1)}$

Work Step by Step

$y=\frac{\ln(5x+1)}{\ln 4}$ $u=\ln(5x+1)$ $u’=\frac{5}{5x+1}$ $v=\ln 4$ $v’=0$ $y’=\frac{u’v-uv’}{v}$ $=\frac{(\frac{5}{5x+1})(ln 4)-(\ln(5x+1))(0)}{(\ln 4)^2}$ $y’=\frac{5}{(ln 4)(5x+1)}$
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