That's how I typically use it (though it has a whole lot more features). Using it in jupyter gives you a notebook environment too, which I really enjoy as I flesh out a problem.

Yes, Sympy is supposed to be an alternative for MAple, Mathematica, sage etc.

You can use it to do so (as an interactive tool).

But it can also be useful as a library, when you develop sth where some symbolic derivation can be useful.