Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 23

Answer

$\sec^2[\ln(ax+b)]*\frac{a}{ax+b}$

Work Step by Step

$\frac{d}{dx}\tan[\ln(ax+b)]$ $=\sec^2[\ln(ax+b)]*\frac{d}{dx}\ln(ax+b)$ $=\sec^2[\ln(ax+b)]*\frac{1}{ax+b}*\frac{d}{dx}(ax+b)$ $=\sec^2[\ln(ax+b)]*\frac{1}{ax+b}*a$ $=\sec^2[\ln(ax+b)]*\frac{a}{ax+b}$
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