If x changes from 4 to 4.01, then find the approximate change in $lo{g}_{e}x$.
 

Let $y=lo{g}_{e}x,x=4,\Delta x=0.01$

$\therefore \frac{dy}{dx}=\frac{1}{x}\Rightarrow dy=\left(\frac{1}{x}\right)dx$        $\Rightarrow dy={\left(\frac{dy}{dx}\right)}_{x=4}\times \Delta x=\frac{1}{4}\times 0.01$

So, $dy=\frac{1}{400}=0.0025$