`x^2y+y^2x=-2`

Differentiating both sides with respect to x,

`x^2d/dx(y)+yd/dx(x^2)+y^2d/dx(x)+xd/dx(y^2)=0`

`x^2dy/dx+y(2x)+y^2+x(2y)dy/dx=0`

`x^2dy/dx+2xydy/dx+2xy+y^2=0`

`(x^2+2xy)dy/dx=-2xy-y^2`

`dy/dx=(-2xy-y^2)/(x^2+2xy)`

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