1. Differentiation Rules and formulas
Chapter 3
Differentiation Rules and formulas
We see from the last chapter, finding a derivative function using the definition involves a long computation. Sometimes, the process is very long and painful.
We could only find derivative functions for simple functions in the last chapter. For general functions, it is hard or even impossible to find their derivative functions by using the definition.

2. Instead of using the definition to compute limits of difference quotients over and over, we do once in general to establish some rules and formulas. Then apply these rules and formulas to compute derivatives.
Note that we are able to find derivative functions using these rules and formulas for general functions not just for simple functions.

3. Computing derivatives is a basic requirement of this course.
You must memorize all these formulas and rules.
You must do a lot of practice in computing derivatives. If you cannot compute derivatives properly, you will not pass this course.

4. §3.1 and §3.2
Differentiation formulas and rules

6. Comment:
We are going to prove all these formulas
later on except (3).
(2) The rigorous proof for (3) is beyond the scope of this book. Here we just provide a rough sketch for the proof: