UNIT IV Derivatives of Products and Quotients Dr
- Slides: 11
UNIT IV Derivatives of Products and Quotients Dr. T. VENKATESAN Assistant Professor Department of Statistics St. Joseph’s College, Trichy-2.
Quotients Products Rule! This lesson will show us how to take derivatives of products and quotients. 2
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 3
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 4
Try It Out Given the following functions which are products • Determine the derivatives 5
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 6
A Memory Trick Given Then
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. 2 A Page 259 Exercises 1 – 33 odd Lesson 4. 2 B Page 260 Exercises 39 – 49 odd 11
- Estimating products and quotients
- Partial quotients
- How to do partial quotient division
- Partial quotients algorithm
- Partial quotients
- Quotients égaux
- Functional products
- Pepsi products vs coke products
- Unit 10, unit 10 review tests, unit 10 general test
- Product and quotient rules and higher order derivatives
- Unit 7 engineered wood products
- Onion pique definition