"Learns enough to do this"... in what sense? If you compare this to a puzzle, are you claiming they have all the pieces, or are you claiming they actually would be able to put the pieces together if you asked them to? The proof steps are tricky, it's not just a straightforward evaluation of some expression.

Also -- are you really claiming every STEM student at your university learns calculus of variations as a freshman? Because that's the only way I've actually seen others prove this. While doing it with plain calculus isn't impossible, it requires a similar kind of thought process that you get after learning calculus of variations, so I'm really skeptical what you're saying is the case, unless you're thinking of a different proof or something.