Derivative of composite function with ln and square root

Question

I need to find $f(x)'$ while $f(x) = ln(x+\sqrt{a^2+x^2})$

I'm having: $f(x)'=\frac{1}{(x+\sqrt{a^2+x^2})}\cdot\left(1+\frac{2x}{2\sqrt{a^2+x^2}}\right)$ ... can't simplify.

I should get $\frac{1}{\sqrt{a^2+x^2}}$. Any suggestions greatly appreciated! :)

Answer 1

Reduce what is inside parenthesis to the same denominator, factor 2, simplify and you get the result.