That’s pretty obvious: Finding derivatives using limits is a pain!

Knowing the derivatives of the common functions makes it easy to find.

No hiding it: you need to memorize these formulas. The best way is to learn them as you get them, a few at a time. I’m sure your teacher will not give them to you all at once. From the first day, memorize them by saying them to yourself as you use them. Don’t wait until the night before the test.

It’s really not too bad: there are only about seventeen formulas for the derivatives of the Elementary Functions. The Elementary Functions as those you’ve learned about already: powers if x including fractional and negative powers (one formula for all), six trigonometric functions, six inverse trigonometric function, exponential functions (one for base e and one for other bases), logarithm functions (natural, and the others).

Formulas are really theorems. The proofs of the formulas are interesting from a mathematical point of view. You should follow along when your teacher shows them to you so that you understand why they work and where they come from. You will not be asked to reproduce the proofs on the AP Calculus Exam.

AP Calculus Course and Exam Description Unit 2 topics 2.5 – 2.7