Undefined function or variable 'dx'.

jacobi = [dx(f1,x1,y1) dy(f1,x1,y1);

dx(f2,x1,y1) dy(f2,x1,y1)]; %jacobian matrix that obtains partial dervatives

[John D'Errico]

You cannot just write dx, and hope that MATLAB will be smart enough to differentiate something. The mindreading toolbox is never working when you need it.

I would strongly suggest you first spend some time with the MATLAB Onramp tutororial. Then spend some time in learnign how to use the symbolic toolbox. diff can differentiate an expression.

[Torsten]

syms x y
f1 = x^2+y^3;
f2 = sin(x) + exp(y);
f = [f1,f2];
jacobian(f)

ans = 

Answer 1

[Aniket]

Hi @Mustafa Abdelfattah,

The error is thrown because `dx` is not a predefined function in MATLAB for differentiation.

Here are two ways to calculate the Jacobian matrix:

1. Using Symbolic Differentiation (`diff`)

% Define symbolic variables
syms x y

% Define the functions
f1 = x^2 + y^2 - 1;
f2 = x^2 - y;

% Compute the Jacobian matrix using symbolic differentiation
jacobi = [diff(f1, x), diff(f1, y); 
    diff(f2, x), diff(f2, y)];

2. Using the Inbuilt `jacobian` Function

% Define symbolic variables
syms x y

% Define the functions
f1 = x^2 + y^2 - 1;
f2 = x^2 - y;

% Create a vector of the functions
F = [f1; f2];

% Compute the Jacobian matrix using the inbuilt function
jacobi = jacobian(F, [x, y]);

Both methods will yield the same Jacobian matrix.

For more information, refer to the following MATLAB documentation

Symbolic differentiation: https://www.mathworks.com/help/symbolic/diff.html

Jacobian function: https:/www.mathworks.com/help/symbolic/sym.jacobian.html

Hope this helps!