The given functions are
[tex]\begin{gathered} f(x)=e^x \\ \\ g(x)=ln(x) \end{gathered}[/tex]
Since we need to find the derivative of g(x)
Then we will use
[tex]x\frac{dy}{dx}=1[/tex]
Divide both sides by x
[tex]\frac{dy}{dx}=\frac{1}{x}[/tex]
Plug in (lnx) for y
[tex]\frac{d}{dx}ln(x)=\frac{1}{x}[/tex]
Then
[tex][ln(x)]^{\prime}=\frac{1}{x}[/tex]
From here we can say
[tex]g^{\prime}(x)=\frac{1}{x}[/tex]
