Answer
$$\frac{dy}{dx}=\frac{y^2+4x}{1-2xy}.$$
Work Step by Step
By differentiating the equation $ y=xy^2+2x^2$ with respect to $ x $, we get
$$\frac{dy}{dx}=y^2+2xy \frac{dy}{dx}+4x\Longrightarrow \frac{dy}{dx}(1-2xy)=y^2+4x $$
and hence
$$\frac{dy}{dx}=\frac{y^2+4x}{1-2xy}.$$
