D[x Exp[-(x^2)-(y^2)]-λ(x+y-0.1), y,y]

Gradiente[x:_ ,y:_, λ:_] =Block[{e, g},
e = N[(E^(-(x^2)-(y^2)))];
g = {e(1-2   (x^2))-λ,-2e x y-λ, 0.1-x-y} ;
g]
Hessiano[x:_, y:_, λ:_] = Block[{e},
e =  N[(E^(-(x^2)-(y^2)))];
h={
{e(-6 x +4 (x^3)),e(-2  y+4  (x^2) y) , -1},
{e(-2  y+4  (x^2) y) , e(-2  x+4  x (y^2)),-1},
{-1, -1, 0}
};
h]

Gradiente[-0.4, 0.5, 0.0] //MatrixForm
Hessiano[-0.4, 0.5, 0.0]//MatrixForm

D[x Exp[-(x^2)-(y^2)]-λ(x+y-0.1), y,y]

x ={-0.4, 0.52,0.1}
H = Hessiano[-0.4, 0.52,0.1]
g = Gradiente[-0.4, 0.52,0.1]
x - Inverse[H].g

C1 = {1/(-0.4+0.52 -0.1), 1/0.52}

A = {{1,1}, {0, 1}}

{{1,1},{0,1}}
{0.45128217009269717, 0.26546010005452775}-100 Transpose[A].C1

100 Transpose[A].C1

100 Transpose[A] C2 A
C2 = {{1/(-0.4+0.52 -0.1)^2,0},{0, (1/0.52)^2}}
{{1.4228661362922688, -0.45128217009269717},{-0.45128217009269717, 0.26546010005452775}}-100 A C2 Transpose[A]