Derivation of F (x) = 2x / x ^ 2 + 1

Derivation of F (x) = 2x / x ^ 2 + 1

F (x) = 2x / x ^ 2 + 1 is the meaning of F (x) = 2x / (x ^ 2 + 1)?
f′(x)=[2(x^2+1)-2x*2x]/(x^2+1)^2
=(2-2x^2)/(x^2+1)^2
The derivation of U / V is: (U ′ V-UV ′) / V ^ 2