Interesting - for symbolic differentiation I imagine it's about code-manipulation rules for e.g. calculus' product rule, chain rule etc.?

Essentially, yes. And if you want it to be pretty, it gets complicated quickly.

https://mitpress.mit.edu/sites/default/files/sicp/full-text/... is the chapter. Turns out it wasn't the "very next" one. But it is in my head.