y=-2x/(1+x^2)^2
y' =-2[(1+x^2)^2 - 4x^2.(1+x^2) ]/(1+x^2)^4
=2(3x^4+2x^2 -1)/(1+x^2)^4
=2(3x^2-1)(x^2+1)/(1+x^2)^4
=2(3x^2-1)/(1+x^2)^3