f'(x)=8(x^2+4)^(-1)
=-8(x^2+4)^(-2)(2x)
=-16x/(x^2+4)^2
f"(x)=-16*[(x^2+4)^2-2(x^2+4)(2x)]/(x^2+4)^4
=-16(x^2+4-4x)/(x^2+4)^3
=-16(x-2)^2/(x^2+4)^3