To me, first-semester calculus is a "big ideas" course, whereas second-semester calculus is about a certain bag of tricks. How much memorization is it appropriate to require in the first semester?
If one gives open-notes and/or open-book exams, then a clear message is sent to the students that it's not all about memorization, and I think that's a good thing. I think instructors often use an overemphasis on memorization in order to keep students happy, since students universally accept a requirement to memorize, but may get very angry about a requirement to think.
But for example I often encounter students who don't remember, one semester later, that the derivative of $e^x$ is $e^x$. This complete lack of technical facility would seem to make it impossible for them to use their calculus for anything. It could be like turning out piano students who can't locate F-sharp on the keyboard.
Is there some basic body of knowledge that a calc student should be expected to memorize? If so, what does it consist of, and what are effective methods for enforcing this expectation? I have at least one colleague who has a short test on calculus facts that requires memorization and that is completely separate from the other tests in the course. Is this a good idea?
To put this another way, suppose that a student who got a C from me in first-semester calc shows up in your second-semester course. Is there a particular fact X such that, if the student didn't know X, you'd curse me for not having high enough standards for a C? In the case where X is $d(e^x)/dx=e^x$, I would think that an A student would understand that this is essentially the whole idea behind the exponential function, and therefore wouldn't have to memorize it -- but this might not be a reasonable expectation for a C student.