Maybe tight is harmful.

The code is unclear because it has single-letter variables instead of names, exacerbated by being in Greek, which mathematicians reached for because they were using single-letter variables, and ran out of them, and weren't bold or imaginative enough to break from convention. Then they used up the best of the Greek letters too and moved on to things like Gothic. This is stupid.

How would you name the variables in the code to make it clearer?

No they didn't use them because they ran out. You know nothing about mathematics clearly. There are conventions to keep it concise. Some definitions of simple things would be unreadable if you used longer names. Consider the quotient rule:

    k'(x)=(g(x)f'(x)-f(x)g'(x))/(g(x)^2

Or in your world apparently

    quotient'(expression)=(left_expression(expression)right_expression'(expression)-right_expression(expression)left_expression'(expression))/(left_expression(expression)^2

Yeah, no.

Surprisingly I've just gone through the last 30 pages of mathematical work I've done and there's a couple of π in ∫ there and that's it.

I'm sorry, but you used ' to denote differentiation.

To have it his way, you'd right:

(derivative(right_expression))(expression)

and so on.

Clear as mud!

Good point. Urgh.

Perhaps he's a LISP programmer and has some spare brackets floating around :-)