1. 3.3 Differentiation Rules Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003

2. If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

3. We saw that if,. This is part of a pattern. examples: power rule

4. examples: constant multiple rule:

5. (Each term is treated separately) constant multiple rule: sum and difference rules:

6. Example: Find the horizontal tangents of: Horizontal tangents occur when slope = zero. Plugging the x values into the original equation, we get: (The function is even, so we only get two horizontal tangents.)

12. First derivative (slope) is zero at:

13. product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

14. quotient rule: or

15. Higher Order Derivatives: is the first derivative of y with respect to x. is the second derivative. (y double prime) is the third derivative.is the fourth derivative. We will learn later what these higher order derivatives are used for. 