Notation for derivatives at a certain point

Question

Is the notation for values of a derivative at some point that I used in this question commonly accepted and understandable? Is there a more preferred one?

For those who familiar with Mathematica — I used the notation $$\left[\frac{\partial J_\nu(x)}{\partial\nu}\right]_{\nu=1/2}$$ to represent an equivalent of Mathematica expression Derivative[1, 0][BesselJ][1/2, x] or, equivalently, Function[ν, BesselJ[ν, x]]'[1/2].

Answer 1

This is not a general answer, but

• It is perfectly understandable to me. And I think most seasoned mathematicians will not mistake it for anything else.
• I would personally usually use the vertical bar for restriction or evaluation, like $$ \left. \frac{\partial J_\nu(x)}{\partial \nu}\right|_{\nu = \frac12} $$ to express what you wrote. But that is just one convention that one sees used sometimes in PDEs and geometry.