f[x_,y_]:=Sin[x*y]-x^2*y;
Dx[f_][x_,y_]:=D[f[u,v],u] /. {u->x,v->y}
Dy[f_][x_,y_]:=D[f[u,v],v] /. {u->x,v->y}
grad[f_][x_,y_]:={Dx[f][x,y,z],Dy[f][x,y,z]};
Dxx[f_][x_,y_]:=D[f[u,v],{u,2}]  /. {u->x,v->y}
Dxy[f_][x_,y_]:=D[D[f[u,v],u],v] /. {u->x,v->y}
Dyy[f_][x_,y_]:=D[f[u,v],{v,2}]  /. {u->x,v->y}
hess[f_][x_,y_]:={{Dxx[f][x,y],Dxy[f][x,y]},{Dxy[f][x,y],Dyy[f][x,y]}}
Q[x_,y_]:=f[1,1]+grad[f][1,1].{x-1,y-1}+(hess[f][1,1].{x-1,y-1}).{x-1,y-1}/2
