f(x)=ln((4+x^2)^1/2/x))
Its the Squ root of 4+x^2 over X
Use chain rule, treat $\displaystyle f(x)= ln(x) $ as your outside function and $\displaystyle g(x)= \frac { \sqrt {4+x^2}}{x} $ as your inside function.
You should have:
$\displaystyle \frac {d}{dx} ( \frac { \sqrt {4+ x^2} }{x}) = \frac {1}{ \frac { \sqrt {4+ x^2 }}{x} } ( \frac {d}{dx} \frac { \sqrt {4+ x^2 }}{x}) = \frac {x}{ \sqrt {4+ x^2 }}( \frac {d}{dx} \frac { \sqrt {4+ x^2 }}{x}) $
Use the quotient rule for the last derivatives.