The derivative of arctan(2x)\arctan(2x)arctan(2x) is:
2/(1+4x2)2 / (1 + 4x^2)2/(1+4x2)
1/(1+4x2)1 / (1 + 4x^2)1/(1+4x2)
2/(1+x2)2 / (1 + x^2)2/(1+x2)
1/(1+2x2)1 / (1 + 2x^2)1/(1+2x2)