derivative of two matrices 2 by 2

If I have a matrix P of size 2 by 2 and a matrix F of size 2 by 2, how do I find the derivative of P with respect to F? Note that P and F are matrices are real numbers.

Is this code is mathmatically correct?

syms F1 F2 F3 F4; % Define symbolic variables for the elements of matrix F

F = [F1, F2; F3, F4]; % Define matrix F

syms p1 p2 p3 p4; % Define symbolic variables for the elements of matrix p

p = [p1, p2; p3, p4]; % Define matrix p

% Calculate the derivative of p with respect to F

dpdF = jacobian(p(:), F(:));

disp(dpdF)

The out put is

[0, 0, 0, 0]

[0, 0, 0, 0]

[0, 0, 0, 0]

[0, 0, 0, 0]

Answer 1

[Sam Chak]

If the four elements in Matrix P do not involve any variables defined in Matrix F, then taking the derivative of the four elements in P with respect to the four variables in F will result in a 4-by-4 array of zeros.

If that is not the case, then you maybe looking for this:

syms F1 F2 F3 F4;   % Define symbolic variables for the elements of matrix F
F   = [F1, F2; 
       F3, F4]      % Define matrix F

F = 

p1  = 1*F1;
p2  = 2*F2;
p3  = 3*F3;
p4  = 4*F4;
p   = [p1, p2; 
       p3, p4]      % Define matrix p

p = 

% Calculate the derivative of p with respect to F
pt  = transpose(p);
Ft  = transpose(F);
dpdF= jacobian(pt(:), Ft(:))

dpdF = 

[Omar Aref]

Thank you Sam Chak , I really appricate your help it really complex for me as alot of variable involved. I need to calculate first Piola–Kirchhoff stress which is defined as derivative of strain energy density with respect to deformation gradient.

[Sam Chak]

You're welcome, @Omar Aref. If there is no efficient way to express the elements in Matrix P, then you will need to input all the variables manually.