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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

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Basic Differentiation Rules

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  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 • DifferenceRule How would you put these rules into words?

  5. Better Try This • Determine the following

  6. 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

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

  8. Derivatives Involving sin, cos • Try the following

  9. 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 ?

  10. Try It Out • Find the derivative

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

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