# Derivative of inverse trig function absolute value?

Find the derivative of y = arctan(x^(1/2)).

Using the fact that the derivative of arctanx = 1/(1+x^2) I got:

dy/dx = 1/(1+abs(x)) * (1/2)x^(-1/2)

But my textbook gives it without the absolute value sign. I don't understand why because surely x^(1/2) squared is the absolute value of x and not simply x?