I believe this will solve your problem:
Differentiate xarctan√x
f'(x)=x*1/(1+((√x)²)*(1/2)x^(-1/2)
= √x/((2(1+x))+arctan√x
My question is this...where did that specific term go? Why is it not in the denominator? I feel as though this is just something I'm not thinking of properly.
Thanks!