What would you like to understand?

The first column of the Jacobian matrix records the output components resulting from an infinitesimal step in the x direction. Specifically, the top entry is the horizontal change in the first output component, and the bottom entry is the vertical change in the second output component, both caused by the x-step.

Conditions: The input perturbation is taken strictly in the positive x direction.; The output is a 2D vector with components $f_1$ and $f_2$.; The step size is infinitesimal, allowing linear approximation.

The first column of the Jacobian matrix records the output components resulting from an infinitesimal step in the x direction. Specifically, the top entry is the horizontal change in the first output component, and the bottom entry is the vertical change in the second output component, both caused by the x-step.

Conditions: The input perturbation is taken strictly in the positive x direction.; The output is a 2D vector with components $f_1$ and $f_2$.; The step size is infinitesimal, allowing linear approximation.