f’(x)=[x-x^3)’(1+2x^2+x^4)-(x-x^3)(1+2x^2+x^4)’]/
(1+2x^2+x^4)^2
=[(1-3x^2) (1+2x^2+x^4)-(x-x^3)(4x+4^3)]/ (1+2x^2+x^4)^2
=(1-5x^2-2x^4+x^6)/ (1+2x^2+x^4)^2
f’(x)=[x-x^3)’(1+2x^2+x^4)-(x-x^3)(1+2x^2+x^4)’]/
(1+2x^2+x^4)^2
=[(1-3x^2) (1+2x^2+x^4)-(x-x^3)(4x+4^3)]/ (1+2x^2+x^4)^2
=(1-5x^2-2x^4+x^6)/ (1+2x^2+x^4)^2