Computation of a Jacobian comes up as a part of many problems. For example, in computation fluid dynamics application, where a numerical approximation of a derivative must be computed at every point on a 1000x1000x1000 grid at every time step, so it is beneficial to speed up the simulation as a whole.
For more details: https://github.com/tvdmitrii/ME759_FinalProject/blob/master/me759DmitriiTurygin.pdf