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Surely there is a way to do this numerically, isn't there? What I mean is that one should be able to write a function which, for a given numerical value of x, solves the implicit equation to find the value of the derivative at x -- using find_root, perhaps. And then one ought to be able to plot this function.

Of course this won't work for every implicitly defined function, but sage's numerics should work for a lot of cases that users actually want.

But I don't know enough about sage symbolics to actually do this. Any takers?