Having mechanical formulae for solving closed form equations involving the notation for derivatives… does not mean that derivatives have been understood, in my experience of tutoring not-especially-mathematically-inclined folks.

Do you think 90% of attendees of Gymnasium (which I don’t think is the majority) understand derivatives? My friend’s wife who attended Gymnasium and got reasonably good grades most certainly did not, but she is my only example of a non-mathematician Gymnasium graduate, so I’m quite willing to be convinced she is an outlier.