how about 2arctan(x)/pi?
Yeah definately as arctan = tan-1 is just an inverted tan function which looks like this:
Except from -1 to 1 instead of from -pi/2 to pi/2 which is why you multiply with 2/pi.
EDIT: Honestly it depends if the derivative in 0 has to be infinity or not. Judging by the picture Squideey drew (where the derivative is infinity in (0,0)) it's neither x/sqrt(1+x²) nor 2arctan(x)/pi. We haven't found it yet guys.
