### 3.1 Basic Rules of Differentiation

__Four Basic Rules of Differentiation:__

__1. Derivative of a Constant:__The derivative of a constant function is always equal to 0.

**Proof:**

__The derivative of a power function is equal to the exponent times the quantity of the variable raised to the power of the exponent minus 1.__

**2. The Power Rule**

**Proof:**

__3. Derivative of a Constant Multiple of a Function__The derivative of a constant time a function is equal to the constant times the derivative of the function.

**Proof:**

__4. The Sum Rule__The derivative of the sum or difference of 2 functions is equal to the sum or difference, respectively, of their derivatives.

**Proof:**

__Example Problem:__Find the derivative of the function

*f*by using the rules of differentiation.

**Links to Derivatives:**

http://archives.math.utk.edu/visual.calculus/2/index.html

http://mathworld.wolfram.com/Derivative.html

**Brian, you're up next with 3.2 The Product and Quotient Rules**

**Derivative Joke:**

Q: What is the first derivative of a cow?

A: Prime Rib!

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