1. 2.2 Basic Differentiation Rules and Rates of Change (Part 1)
Colorado National Monument
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2003

2. Objectives Find the derivative of a function using the Constant Rule.
Find the derivative of a function using the Power Rule.
Find the derivative of a function using the Constant Multiple Rule.
Find the derivative of a function using the Sum and Difference Rules.
Find the derivative of the sine function and of the cosine function.

3. Rate of Change

4. 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.

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

6. Examples:

7. Example
Find the slope of the graph of f(x)=x4 when (a) x= -1, (b) x=0 and (c) x=1.

8. Example
Find an equation of the tangent line to the graph of f(x)=x2 when x= -2.

9. constant multiple rule:
examples:

10. Examples: Find the derivative

11. Examples: Find the derivative

12. Examples: Find the derivative

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

14. Sine and Cosine rules:

15. Homework
2.2 (page 115)
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