Oh interesting. If I understand what you mean by that, it’s reading your code, translating it into something that a tool like Mathematica/Wolfram Alpha can read as an equation and then having the Mathematica-like tool take the derivative of that. Is that roughly correct?
I don’t really know how the internals of symbolic differentiation works, but my first guess would be that it does something like apply the chain rule a whole lot, which I would think is functionally very similar to auto-differentiation (although all these topics I only vaguely understand from the outside). If I’m wrong about that, then the real answer is “you just need to learn more about CAS systems” and I assume you’re not going to put up a full intro to CAS in a Julia Discourse thread 