Calculus has many applications. ;-) One thing people might be able to use this for is algebraically derived first or second derivatives (or their matrix forms gradients and Jacobians, Hessians). While few statements can be absolute, typically algebraic forms are both faster to evaluate and more accurate than numerical derivatives. That can help things like numerical minimization (eg. for non-linear least squares, etc.) and equation solving.
There are also things like [Complex Step Differentiation](https://rdrr.io/cran/pracma/man/complexstep.html), of course, with its own peculiar needs. Arraymancer probably has some autograd stuff in it as well, but I don't know how tangled up that is in the highly idiosyncratic backprop algorithm.
