1. 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. 3.3 Basic Differentiation Formulas

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 Power Rule

4. Don’t forget it! Special Case? – or just obvious Power Rule

5. examples: Constant multiple rule:

6. (Each term is treated separately) Sum and Difference rules:

7. 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.)

13. First derivative (slope) is zero at:

14. Find the tangent line of the curve y = x + at x = 1. F(1) = 3 so p(1,3), F’(x) = 1 - then M = F’(1) = -1 so the tangent line is y = 3 – (x -1) So Y = -x + 4.

15. 3.4 The Product and Quotient Rules

16. Product Rule The first times the derivative of the second plus the second times the derivative of the first

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

18. Product rule

19. Product rule Example 2

20. Now Simplify and reduce. Quotient Rule

21. ……. The bottom times the derivative of the top minus the tope times the derivative of the bottom all over the bottom squared. Quotient Rule

22. Quotient Rule

23. Find if Exercise