Vector field plot

plotdf([2*x,-2*y]);

Implicit surface

draw3d(enhanced3d=true,
        implicit(x^2-y^2+x*y*z=1,
                 x,-5,5,y,-5,5,z,-5,5),
        surface_hide=true);

Tangent plane to the surface

draw3d(color=blue,
        implicit(x^2-y^2+x*y*z=1,
                 x,-5,5,y,-5,5,z,-5,5),
       color=red,
       explicit(3-3*x+y,x,0,2,y,0,2),
        surface_hide=true);