Trying to run a differentiation loop

I have a matrix X_dot =

3*g*k*x1*t^2 - 2*g*k*x1*t - k*x2

g*x1 - 2*g*t*x1

0

Another matrix, x =

[x1, x2, x3]

when I run these codes separately:

diff(X_dot(2,1),x(1,1))

diff(X_dot(1,1),x(1,1))

I get good answers. But when I put it in a loop, I get weird conversion errors.

My loop looks like this:

L2 = zeros(3)

for r = 1:3
    for c = 1:3
        L2(r,c) = diff(X_dot(c,r),x(r,c));
    end
end

The aim is to differentiate each row of X_dot by each column of x and get a 3x3 matrix output in symbolic form

This is the whole code:

clear all

clc

%%Ans1

syms X1 X2 X3 k t g x1 x2 x3

eqn1 = X1 + (k*t*X2) == x1;

eqn2 = (g*((t-1)*(t*X1))) + ((1+ (g*k)*((t-1)*(t^2)))*X2) == x2;

eqn3 = X3 == x3

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [X1, X2, X3])

X = linsolve(A,B)

F = [1 k*t 0;(g*t)*(t-1) g*k*t^2*(t - 1)+1 0;0 0 1]

J = det(F)

F_inv = inv(F)

%%Ans3

F_d = simplify(diff(F,t))

L = simplify(F_d*F_inv)

expand(L(2,1))

X_dot = diff(X,t)

L2 = zeros(3)

x = [x1,x2,x3]

diff(X_dot(2,1),x(1,1))

for r = 1:3

for c = 1:3

L2(r,c) = diff(X_dot(c,r),x(r,c));

end

end

L2

Please help

[KSSV]

Copy the full code here.

[Saim]

Post is updated with the whole code, hope that helps

Answer 1

[Torsten]

clear all
clc
%%Ans1
syms X1 X2 X3 k t g x1 x2 x3
eqn1 = X1 + (k*t*X2) == x1;
eqn2 = (g*((t-1)*(t*X1))) + ((1+ (g*k)*((t-1)*(t^2)))*X2) == x2;
eqn3 = X3 == x3;
[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [X1, X2, X3]);
X = linsolve(A,B);
F = [1 k*t 0;(g*t)*(t-1) g*k*t^2*(t - 1)+1 0;0 0 1];
J = det(F);
F_inv = inv(F);

%%Ans3
F_d = simplify(diff(F,t));
L = simplify(F_d*F_inv);
expand(L(2,1));

X_dot = diff(X,t);
%L2 = zeros(3);
x = [x1;x2;x3];
diff(X_dot(2,1),x(1,1))

ans = 

for r = 1:3
    for c = 1:3
        L2(r,c) = diff(X_dot(r,1),x(c,1));
    end
end
L2

L2 =