I go to all the lectures, and lectures are for the most part useless. The professor spends the entire lecture deriving the same equations the book does and doesn't really teach the concepts. However, I don't want to blame the prof for my incompetence and lack of intelligence, since there are many students in the class who are doing well.
I just think I am not getting this stuff, since as you say, it should take 4 and a half minutes to do that problem.
I don't know why people keep saying that doing problems will alleviate this problem, but I'm just not seeing that? I spend hours doing problems, and my problem-solving abilities don't seem to improve as much as people seem to suggest around here. At best, I think I could probably solve the problem in 6 minutes, and that's rushing through it...
I can't really comment on the professor or you, but based on what you have said the professor is actually at least in part, teaching you the concepts.
The idea for things like physics, applied mathematics, statistics and to some degree pure mathematics is that you start off with really general concepts and then you take a lot of them and meld them together with a bunch of constraints to get either a model or a new concept to use.
The idea of doing derivations is not only for the sake of proving results: it's also used to go through what the concepts are and how they play a role in some new result, model or similar representation.
What you should be paying really close attention to is not only what these constraints are and what they mean 'in english' or your language of choice, but also what these constraints mean physically and what the melded formula means physically when it has been proven if your professor is doing so.
I recommend you thinking about your identities and other things like formulas and otherwise in terms of a constraint because if you understand the boundary of that constraint and the consequences of that constraint in terms of physical intuition, it will make your life a lot easier when you see a derivation because in the back of your mind you have mentally prepared yourself by understanding what these formulas mean not in terms of something symbolic mathematically, but symbolic in an intuitive physical sense.
In fact this is precisely what applied mathematicians, physicists and engineers have to do: they take models developed usually by pure mathematicians (often decades or many decades previously) and then they enforce constraints that allow them to make use of a result that was more general but is now simpler to use for the purposes of the scientist, engineer, or otherwise.
The constraint will tell you a lot about what's going on even if you are not an expert or have studied something in a lot of detail if you try and relate the constraint back to what its being used for.
Constraints make it possible for us to understand the world. Without them we wouldn't understand anything because we would be taking in everything and it wouldn't be manageable.