I'm a tutor for a course on optimization at my uni and today (while correcting exercise sheets) a student presented me with something like this: $$ 0 = (ax^* + b) \frac{\partial}{\partial x} $$
Where he put the differential operator behind the expression that he was supposed to differentiate.
Is this just notation convention? Are you allowed to do this?
I searched the internet for this and couldn't find anything.