> But if all it is is converting a Derivative into some expression,
> couldn't the whole thing be done with a single call to .replace()?  I
> suppose things get a little more tricky than that for higher order
> derivatives, but not by much.

I think that the original idea was to *generate* the expression, often
called the "difference stencil", automatically. Something like

  >>> make_stencil(D(f(x), x), order=2)
  (f[i+1] -2 * f[i] + f[i-1]) / (2*h)

but for arbitrary order and also multivariate D. This is just
something that's very error prone when done by hand.

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