## Calculus 8th Edition

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