Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 32

Answer

$f'(x)=\frac{1}{2xln10}$

Work Step by Step

If we first simplify the given function using the properties of logarithms $\frac{d}{dx}(log_{e}(x))=\frac{1}{xlne}$ Then the differentiation becomes easier: $f'(x)=\frac{1}{\sqrt x ln 10}\frac{d}{dx}(\sqrt x)$ $= \frac{1}{\sqrt x ln 10}\frac{1}{2\sqrt x}$ Simplify. Hence, $f'(x)=\frac{1}{2xln10}$
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