I get the idea of Jacobian matrices. I think. Working through different examples, I don't have any problems.
For example,
f1 = x^2 + y^2
f2 = 3x + 4y
would result in
[2x 2y]
[3 4]
Similarly, by my understanding, something like
x^2 + y^2
3y + 4x
would result in
[2x...