Differentiate an implicit linear-product relation

Implicit differentiation gives $1+xy^{\prime}+y-2y^{\prime}=0$. Therefore $(x-2)y^{\prime}=-(1+y)$ and $y^{\prime}=(1+y)/(2-x)$, the printed answer.

The relation gives $y=(5-x)/(x-2)$ for $x\ne2$. At $x=2$, the original equation would say $2=5$, so no point was lost. Explicit differentiation gives $-3/(x-2)^2$, agreeing with the printed implicit form after substituting for $y$.