Derivatives of Products and Quotients

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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 - PowerPoint PPT Presentation

Text of Derivatives of Products and Quotients

  • Derivatives of Products and QuotientsLesson 4.2

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

  • ReviewWe know what to do with constant times a functionFor k f(x)

    We also know what to do with the sum of functionsWhen

    Then*

  • Product RuleConsider 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*

  • Try It OutGiven the following functions which are productsDetermine the derivatives*

  • Quotient RuleWhen 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*

  • OK Try That!Use the quotient rule on the following functions*

  • Average CostSuppose 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 *

  • Average CostSuppose 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*

  • AssignmentLesson 4.2APage 259Exercises 1 33 odd

    Lesson 4.2BPage 260Exercises 39 49 odd*