1. 2.3 Differentiation Rules Colorado National Monument Larson, Hostetler, & Edwards

2. Review Old Topics to Build On: Derivative of a Constant Rule Power Rule 2 Short-cut Rules (Simple Square Root and Reciprocal ) Constant Multiplier Rule New Topics: Product Rule Quotient Rule Higher Order Derivatives Read pages 116 - 1126

3. 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. Review

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

5. There are two simple shortcuts that evolve from the Power Rule, the first is the example: Simple Square Root Rule Review

6. The second of the two simple shortcuts that evolve from the Power Rule is the Simple Reciprocal Rule. example: Simple Reciprocal Rule Review

7. examples: constant multiple rule: Review

8. sum and difference rules:

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

10. Example:

11. quotient rule:

12. Applications of Derivatives: 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.)

18. First derivative (slope) is zero at:

19. 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. 

20. Assignment: page 124 - 125 Part - 1: Do 1 – 35 odds, 38, 40, 47 Part – 2: Do 2 – 36 evens, 37, 39, 42