Question

X^3-2y^3+xy(2x-y)+y(x-y)+1=0

Answer 1

Incomplete question:

No information is given that what needs to done here.

Let us solve for the derivative w.r.t $x$ :

Let $f(x,y)=x^3-2y^3+xy(2x-y)+y(x-y)+1\\$

$=x^3-2y^3+2x^2y-xy^2+xy-y^2+1$

$f_x=\frac{\partial}{dx}[x^3-2y^3+2x^2y-xy^2+xy-y^2+1] \\ =3x^2+4xy-y^2+y$