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.
k'(x)=(g(x)f'(x)-f(x)g'(x))/(g(x)^2
quotient'(expression)=(left_expression(expression)right_expression'(expression)-right_expression(expression)left_expression'(expression))/(left_expression(expression)^2
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.
To have it his way, you'd right:
(derivative(right_expression))(expression)
and so on.
Clear as mud!
Perhaps he's a LISP programmer and has some spare brackets floating around :-)