To solve this problem, we have to use implicit derivation. To do it, derive each expression as usual and multiply by y' each expression that contains y, this way:
[tex]\begin{gathered} 4+xy=y^2 \\ y+xy^{\prime}=2yy^{\prime} \end{gathered}[/tex]
Now, solve the obtained equation for y':
[tex]\begin{gathered} xy^{\prime}-2yy^{\prime}=-y \\ y^{\prime}(x-2y)=-y \\ y^{\prime}=-\frac{y}{x-2y} \\ \frac{dy}{dx}=-\frac{y}{x-2y} \end{gathered}[/tex]
