Symbolic derivatives are one of the very next sections in the famous lisp lectures that this was watching.
Re:Not Lisp again (2009)
by QuadrupleA on Friday October 26, 2018 @06:30PM
(#18313176)
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.
Here's symbolic differentiation done in ~20 lines of Haskell: https://www.quora.com/What-are-20-lines-of-code-that-capture...
Maybe that's the misunderstanding in the original article that made it seem so mindblowing?
Evaluating (f(5.0001) - f(5.0)) / 0.0001 just gives an approximation of the derivative at a certain point in the function (aka the "finite difference method").