Step $2$

Differentiate the equation $x^{2}yx{y}^2=0$ with respect to $x$ and solve for $y^{\text{'}}.$

$x^{2}yx{y}^2=0$

$x^2{y}^{\text{'}}2xy{y}^2=0$

$(x^{2}2xy)y^{\text{'}}=-(y^{2}2xy)$

$y^{\text{'}}=\frac{-(y^{2}2xy)}{(x^{2}2xy)}$

$=-\frac{y(y2x)}{x(x2y)}$