Find the derivative. F(x)=x^4+x^2+1/(x^2+1)

I have a hunch you mean:

(x^4+x^2+1)/(x^2+1)

(bottom d top - top d bottom)/bottom squared

[ (x^2+1)(4x^3+2x) -(x^4+x^2+1)(2x)]/(x^2+1)^2

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

[2x^5+8x^3+4x]/(x^4+2x^2+1