Plot derivative of a function

[Manolo Sobrino]

(06-08-2014 01:00 PM)parisse Wrote:  Maths notations are most of the time context-sensitive (e.g. f(x+1) vs y(x+1)). I do not remove points to a student writing int(f(x),x,0,x) if he is at a sufficient level.

Yes, they are context dependent, but in an expression same symbols should refer to the same thing as x=x and we all agree on Leibniz's law. You can use for instance an i for the imaginary number and an index, the context makes it clear -they are different things- but that's because we don't use the imaginary unit for indexes because that makes no sense and free standing indexes are rare. It could be argued that this is still a bad notation, and that's why it is becoming frequent to type the imaginary unit with a different font style.

Using x as a single name for two unrelated variables is troublesome. Not for humans that know what's going on, but for computers. A nice custom (that should be compulsory) is to prime the integration variable so that you have g(x)=int(f(x'),x',0,x).. and thank God they came up with that as a notation for the sources of potentials/fields in contrast with the 'unprimed' variables (those of the potentials/fields).

The point here is that the definite integral cannot depend on the integrated variables because you integrate them! What you are doing is using two different variables called x, one refers to all the points whose value you have to add along the path and after the sum they're done, the other specifies the point at which you stop. You know this, students that have passed some Calculus should as well but the computer doesn't and as I pointed out in another thread IMO it can cause trouble with delayed evaluation.