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