Having mechanical formulae for solving closed form equations involving the notation for derivatives… does not mean that derivatives have been understood, in my

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.