I remember that, as a student, I felt a bit uncomfortable because I had to use the same notation (say $f'$, $D^\alpha f$, $\frac{\partial f}{\partial x^j}$, $\nabla \times f$$\nabla \cdot f$ etc...) for classical and weak derivatives/differential operators, so that, if I wanted to be accurate, I always had to specify in words something like "where the derivative is meant in the weak sense".
As a researcher, I forgot this feeling of unease, because usually everything is clear from the context. In fact it's quite hard to devise an example in which the confusion is actually dangerous.
But then again, as a teacher, I gradually started to feel the need for a clearer notation, because when I talk to students, for purely pedagogical reasons, I'd like to make it crystal clear what I'm talking about. This is especially important precisely at the beginning, when you, introducing Sobolev spaces, have to define what a weak derivative is and how its existence should not be confused with the existence a.e. of the classical derivative.
So I wonder: is there a more or less established, effective notational tool to help distinguishing the weak derivative from the classical one?