How can I solve a Lagrange equation?

Dear all,

I need to solve a Lagrange equation. How can I get derivate of a function in MATLAB?

The equations are;

g=x_1+x_2+x_3 - 10

L=λ*g+V=12*x_1-x_1^2+8*x_2-x_2^2+18*x_3-3*x_3^2+λ*x_1+λ*x_2+λ*x_3-10*λ

what I want to do is find the derivates;

∂L/(∂x_1 )=0

∂L/(∂x_2 )=0

∂L/(∂x_3 )=0

∂L/(∂λ)=0

and finally find the values of x_1, x_2 , x_3 , λ , L and V.

Answer 1

[Torsten]

syms x1 x2 x3 lambda
g = x1+x2+x3 - 10;
L = 12*x1-x1^2+8*x2-x2^2+18*x3-3*x3^2+lambda*g;
Lx1 = diff(L,x1);
Lx2 = diff(L,x2);
Lx3 = diff(L,x3);
Llambda = diff(L,lambda);
s = solve([Lx1==0,Lx2==0,Lx3==0,Llambda==0],[x1 x2 x3 lambda])

s = struct with fields:
        x1: 33/7
        x2: 19/7
        x3: 18/7
    lambda: -18/7

Lopt = subs(L,[x1,x2,x3,lambda],[s.x1,s.x2,s.x3,s.lambda])

Lopt = 

[Sena]

Thank you so much for your answer, it helped a lot.