Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 26

Answer

$\frac{1}{2t\sqrt{1+\ln t}}$

Work Step by Step

$\frac{d}{dt}\sqrt{1+\ln t}$ $\frac{d}{dt}(1+\ln t)^\frac{1}{2}$ $=\frac{1}{2}(1+\ln t)^{-\frac{1}{2}}\frac{d}{dt}(1+\ln t)$ $=\frac{1}{2\sqrt{1+\ln t}}*\frac{1}{t}$ $=\frac{1}{2t\sqrt{1+\ln t}}$
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