1. 1 Basic Differentiation Rules Lesson 3.2A

2. 2 Basic Derivatives Constant function – Given f(x) = k Then f’(x) = 0 Power Function –Given f(x) = x n Then

3. 3 Try It Out Use combinations of the two techniques to take derivatives of the following

4. 4 Basic Rules Constant multiple Sum Rule Difference Rule How would you put these rules into words?

5. 5 Better Try This Determine the following

6. 6 An Experiment Enter the difference quotient function into your calculator Now graph the function and see if you recognize it Looks like the cosine function to me, pardner!

7. 7 Conclusion We know that the limit of the difference function as h  0 is the derivative Thus it would appear that for f(x) = sin x f ‘ (x) = cos x Make a similar experiment with the cosine function –What is your conclusion?

8. 8 Derivatives Involving sin, cos Try the following

9. 9 Derivative Rule for e x Experiment again … –Graph both –Make sure to set style on difference function to “Path” What is your conclusion about ? Shazzam! Looks like e x is its own derivative! Shazzam! Looks like e x is its own derivative! Let’s look at that Geogebra demo Let’s look at that Geogebra demo

10. 10 Try It Out Find the derivative

11. 11 Assignment Lesson 3.2A Page 136 Exercises 1 – 65 EOO