In math, the general mantra should be to prioritize the "how" and the "why" over the "what". This means, instead of memorizing facts, make sure you understand exactly why they are true and how to arrive at them.
In Calculus, however, there are so many facts to remember that you can't possibly store the proof of every single one in your brain if you don't spend time revising them. This is a reference table of common and basic derivative problems that you need to know by heart in order to continue to the next lesson.
Do yourself a favor and don't memorize these. Don't make flashcards, don't make a Quizlet, don't... you get the idea. Instead, go to the lessons where they were proved and read the proof again and again until you think that you can do it without looking at the proof. Then, do exactly that until you can.
The purpose of this reference table is only to provide you with a list of what is most important for you to know. Do not treat it like a dictionary.