1. ## derivative

f(x)=ln((4+x^2)^1/2/x))

Its the Squ root of 4+x^2 over X

2. Use chain rule, treat $f(x)= ln(x)$ as your outside function and $g(x)= \frac { \sqrt {4+x^2}}{x}$ as your inside function.

You should have:

$\frac {d}{dx} ( \frac { \sqrt {4+ x^2} }{x}) = \frac {1}{ \frac { \sqrt {4+ x^2 }}{x} } ( \frac {d}{dx} \frac { \sqrt {4+ x^2 }}{x}) = \frac {x}{ \sqrt {4+ x^2 }}( \frac {d}{dx} \frac { \sqrt {4+ x^2 }}{x})$

Use the quotient rule for the last derivatives.