The document discusses the definition and rules for calculating derivatives of various types of functions, including linear functions, constant functions, constant times a function, sums and differences of functions, and power functions. Formulas are provided for taking the derivative of each type, along with examples of applying the rules to find specific derivatives. Proofs of the rules are also presented.

1. Derivatives Rule! Even dogs can do it ...
NooNoo studying calculus

2. The Definition of a Derivative
Mathematics is the science of pattern ... let's look for some patterns ...
Let's use the definition to find some derivatives ...

3. The Derivative of a Linear Function
If then
Proof:
Example: Find the derivative of

4. The Derivative of a Constant Function
If then
Proof:
Example: Find the derivative of

5. The Derivative of a Constant Times a Function
Proof:
Example: Find the derivative of

6. The Derivative of a Sum of Functions
Proof:

7. The Derivative of a Difference of Functions
Proof:

8. The Derivative of a Power Function
Proof:

10. Example: Find the derivative of