1 Basic Differentiation Rules Lesson 3.2A

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

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

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

5 Better Try This Determine the following

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 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 Derivatives Involving sin, cos Try the following

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 Try It Out Find the derivative

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