Basic Differentiation Rules

Basic Differentiation Rules Lesson 3.2A

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

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

Basic Rules • Constant multiple • Sum Rule • DifferenceRule How would you put these rules into words?

Better Try This • Determine the following

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

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 xf ‘ (x) = cos x • Make a similar experiment with the cosine function • What is your conclusion?

Derivatives Involving sin, cos • Try the following

Let’s look at that Geogebra demo Shazzam! Looks like ex is its own derivative! Derivative Rule for ex • Experiment again … • Graph both • Make sure to set style on differencefunction to “Path” • What is your conclusion about ?

Try It Out • Find the derivative

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

Basic Differentiation Rules

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