Let $F(x,y)=($:$P(x,y),Q(x,y)$:$),$ where

$P(x,y)==\frac{2x}{y^2+1},Q(x,y)==-\frac{2y(x^2+1)}{(y^2+1{)}^2}$

$(a)$ Determine $ifFis$ a conservative vector field.

$(b)IfFis$ conservative, find a potential function $f(x,y)$ such that gradf$=F.$