UNIT IV Derivatives of Products and Quotients

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Presentation transcript:

UNIT IV Derivatives of Products and Quotients Dr. T. VENKATESAN Assistant Professor Department of Statistics St. Joseph’s College, Trichy-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 When Then

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

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

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

A Memory Trick Given Then

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

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

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

Assignment Lesson 4.2A Page 259 Exercises 1 – 33 odd Lesson 4.2B