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Derivatives of Products and Quotients

Derivatives of Products and Quotients. Lesson 4.2. Quotients Rule!. Products Rule!. This lesson will show us how to take derivatives of products and quotients. Review. We know what to do with constant times a function For k • f(x) We also know what to do with the sum of functions

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Derivatives of Products and Quotients

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  1. Derivatives of Products and Quotients Lesson 4.2

  2. Quotients Rule! Products Rule! This lesson will show us how to take derivatives of products and quotients.

  3. Review • We know what to do with constant times a function • For k • f(x) • We also know what to do with the sum of functions • When • Then

  4. Product Rule • Consider the product of two functions • It can be shown (see proof, pg 215) that • In words: • The first function times the derivative of the second plus the second times the derivative of the first

  5. Try It Out • Given the following functions which are products • Determine the derivatives

  6. Quotient Rule • When our function is the quotient of two other functions … • The quotient rule specifies the derivative • In words: • The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator

  7. OK … Try That! • Use the quotient rule on the following functions

  8. Average Cost • Suppose we have a function y = C(x) which gives us the cost of manufacturing x items • The average cost is • Then the marginal average cost is

  9. Average Cost • Suppose the cost for manufacturing x items is • Write the function for the average cost • What is the marginal average cost? • Determine rate of change of the average cost for 5 items … for 50 items

  10. Assignment • Lesson 4.2A • Page 259 • Exercises 1 – 33 odd • Lesson 4.2B • Page 260 • Exercises 39 – 49 odd

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