In reply to @icecolbeveridge
@icecolbeveridge @hartkp it could, but my point was about how awkward expressions with lots of terms look. I'm sure there's been some cognitive science done about this.
In reply to @christianp
@icecolbeveridge @hartkp You also encounter problems when trying to write down the general formula: how do you write the differential operator? And then, how do you write the derivative of the composition of two functions? I think you end up needing a function application operation