use C++ autodiff to do Jacobians

[zingale]

Instead of hand-coding the Jacobians, we should explore using a C++ autodiff package, e.g.,

https://autodiff.github.io/

to construct the analytic Jacobians.

[maxpkatz]

Some aspects of this were addressed in #624 which automatically computes the derivatives with respect to Y in the Jacobian terms. However (at least for the aprox rates) we are still relying on analytical expressions for the d/dT terms, so there is still some possibility for improvement here.