Creating the derivative function of my complex function

Greetings,

Im trying to create the derivative function of my own build which, which is quite complex.

Ive have tried using this:

function Beta_Derivative = Derivative_Steady_State(Lambda)
Beta_Derivative = diff(Steady_State(Lambda))
end

However this just gives an empty set as awnser, and if i plot my function it need to have a logical awnser for Lambda [0,2].

my function is:

function Beta = Steady_State(Lambda)
P0 = exp(-Lambda)
P1 = Lambda*exp(-Lambda)
P2 = (Lambda^(2)*exp(-Lambda)/2)
P3 = (Lambda^(3)*exp(-Lambda)/6)
b_NN = [100; 85; 75; 65; 55; 50; 45; 40; 35; 33; 31; 29; 27; 25; 23; 21.5; 20; 18.5; 17; 16; 15]

bonusmalus_NN = [1-P0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,;
    1-P0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0-P1,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0-P1,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0-P1,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0,0;
    1-P0-P1,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0,0;
    1-P0-P1,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0,0;
    1-P0-P1-P2,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0,0;
    1-P0-P1-P2,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0,0;
    1-P0-P1-P2,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0,0;
    1-P0-P1-P2,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0,0;
    1-P0-P1-P2,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0,0;
    1-P0-P1-P2-P3,P3,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0,0;
    1-P0-P1-P2-P3,0,P3,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0,0;
    1-P0-P1-P2-P3,0,0,P3,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0,0;
    1-P0-P1-P2-P3,0,0,0,P3,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,0,P0;
    1-P0-P1-P2-P3,0,0,0,0,P3,0,0,0,0,P2,0,0,0,0,P1,0,0,0,0,P0]

[V,A] = eig(bonusmalus_NN)
V_inv = inv(V)
p_lim = V*A^10000000*V_inv
p_lim = p_lim(1,:)

Beta = abs(p_lim * b_NN)
end

So is it possible to create another function which is the derivative function of this?

Kind Regards,

Matthias