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: 8

Answer

$\frac{1}{2x\ln 10}$

Work Step by Step

$\frac{d}{dx}\log_{10}\sqrt{x}$ $=\frac{1}{\sqrt{x}\ln 10}\frac{d}{dx}\sqrt{x}$ $=\frac{1}{\sqrt{x}\ln 10}\frac{1}{2}x^{-\frac{1}{2}}$ $=\frac{1}{\sqrt{x}\ln 10}\frac{1}{2\sqrt{x}}$ $=\frac{1}{2x\ln 10}$
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