Jacobian Matrix is a matrix which stores all the partial derivatives for multiple functions.
For example, let’s consider ex1 (top left). F(x) is a function containing 1 variable. If you calculate the derivative of F(x) it would be 2x.
Now, let’s see ex2. This time F(x,y) is a function containing 2 variables, and if you calculate the derivative of F(x,y), the value would be 2xy and x^2(using the chain rule).
Finally, if you have multiple functions, you can calculate all the partial derivatives, like in the previous steps, and store them into a matrix. This can be helpful when calculating during the back-propagation phase.