[tex]\bf x^3y+3xy^3=x+y\\\\
-----------------------------\\\\
\left[ 3x^2y+x^3\frac{dy}{dx} \right]+3\left[ 1\cdot y^3+x\cdot 3y^2\frac{dy}{dx} \right]=1+\frac{dy}{dx}
\\\\\\
3x^2y+x^3\frac{dy}{dx}+3y^3+9xy^2\frac{dy}{dx}-\frac{dy}{dx}=1\impliedby \textit{common factor}
\\\\\\
\cfrac{dy}{dx}(x^3+9xy^2-1)+3x^2y+3y^3=1
\\\\\\
\cfrac{dy}{dx}(x^3+9xy^2-1)=1-3x^2y-3y^3
\\\\\\
\cfrac{dy}{dx}=\cfrac{1-3x^2y-3y^3}{x^3+9xy^2-1}[/tex]
