Help for automatic differentiation

I am struggling to implement automatic differentiation in a plug-in library... can anybody help? No one has ever tried to add it at all, and it is a pain to find the derivative or the integral by hand.

The Deriv class in jlb.ulb does first and second derivatives of simple functions to a power, such as sin(z)^n. Other functions could be added.

These derivatives are courtesy of https://www.derivative-calculator.net/

But what if there was a way to apply the algorithms of automatic differentiation from https://github.com/autodiff/autodiff

Someone would need to write an UF equivalent which is definitely possible (albeit not with the nice syntax that you get in modern C++).

Then I had something in my head, a neuron activation of sorts: what if we used dual numbers, as well as nodes, forward mode and reverse mode autodifferentiation in UF?

So where do we begin, @ultrafractal ? First of all, we can think of a few ways to accomplish this: through nodes, for example.