The obvious answer is via Sage and SymPy, which will do differentiation and integration symbolically to some degree.

http://www.scipy-lectures.org/advanced/sympy.html#differentiation

However even plain old core Python helps in that students get a sense of functions as top-level citizens. I'm not saying Python is alone in providing this.

If the C language could be written:

function func(function f1, function f2):{ }

with type function both eaten and returned, then we could use C for this kind of thing also.

http://mathforum.org/kb/message.jspa?messageID=10168568  (more on this general topic)

The repl below (you may skip modal window) shows my latest slimmed down version of Compose, something I introduce to the O'Reilly course as well.

https://repl.it/HxMo/2

Function type objects don't ordinarily multiply but what if we want to write h = f * g instead of h(x) = f(g(x)). 

For one thing, why mention x at this point (the argument object) as we're simply defining a function, not calling it with an input right?

The Compose class is just the ticket, swallowing and wrapping a function with a __mul__ API. Now * is your compose operator.  Or use __matmul__ for @ symbol.

Note then, the use of Compose as a class decorator to the same end.

Feel free to recycle this animal in your own lesson plans.  MIT license or whatever.

Kirby

PS:  one of the Pycon keynotes was about the affordability of nuke energy, with the claim / calculation that it's less risky to workers than coal.  I didn't have time to go up to the podium after and listen in on the conversation. We should have started a BOF.  Simulating / modeling risk is something I'm into through CERM Academy.  We could start a thread on Facebook.

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