Differentiation Business Mathematics ppt

Business Mathematics Chapter Differentiation

1. Differentiation Session 9 Course : MATH6135 -Business Mathematics Effective Period: September 20 20

2. Thank you

3. These slides have been adapted from: Haeussler , Jr. E.F., Paul, R. S., Wood, R. J. (2019). Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. 14th. Ontario: Pearson. Chapter 11 Acknowledgement

4. Learning Outcomes After studying this chapter, the students should be able to : LO 1: Identify the concept of mathematics in business decision making LO 2: Explain the mathematics analysis concept properly in business decision making LO 3: Apply mathematics concept and critical thinking to solve economics and business problem in business decision making

5. Introductory Mathematical Analysis For Business, Economics, and The Life and Social Sciences Fourteenth Canadian Edition Chapter 11 Differentiation Copyright © 2019 Pearson Canada Inc. All rights reserved.

6. Chapter Outline 11.1) Differentiation Formulas 11.2) Rules for Differentiation 11.3) The Derivative as a Rate of Change 11.4) The Product Rule and the Quotient Rule

7. 11.1 Differentiation Formulas

8. 11.2 Rules for Differentiation (1 of 7) Below are some rules for differentiation: BASIC RULE 1 Derivative of a Constant: BASIC RULE 2 Derivative of x n : COMBINING RULE 1 Constant Factor Rule: COMBINING RULE 2 Sum or Difference Rule:

9. 11.2 Rules for Differentiation (2 of 7) Example 1 – Derivatives of Constant Functions

10. 11.2 Rules for Differentiation (3 of 7) Example 3 – Rewriting Functions in the Form x a

11. 11.2 Rules for Differentiation (4 of 7) Example 5 – Differentiating Sums and Differences of Functions

12. 11.2 Rules for Differentiation (5 of 7) Example 5 – Continued

13. 11.2 Rules for Differentiation (6 of 7) Example 5 – Continued

14. 11.2 Rules for Differentiation (7 of 7) Example 7 – Finding an Equation of a Tangent Line

15. Exercise Differentiate the functions

16. 11.3 The Derivative as a Rate of Change ( 1 of 3 ) Applications of Rate of Change to Economics

17. 11.3 The Derivative as a Rate of Change ( 2 of 3 ) Example 7 – Marginal Cost

18. 11.3 The Derivative as a Rate of Change ( 3 of 3 ) Example 9 – Relative and Percentage Rates of Change

19. 11.4 The Product Rule and the Quotient Rule (1 of 6 ) COMBINING RULE 3 The Product Rule: COMBINING RULE 4 The Quotient Rule:

20. 11.4 The Product Rule and the Quotient Rule (2 of 6 ) Example 1 – Applying the Product Rule

21. 11.4 The Product Rule and the Quotient Rule ( 3 of 6 ) Example 5 – Applying the Quotient Rule

22. 11.4 The Product Rule and the Quotient Rule ( 4 of 6 ) Example 7 – Differentiating Quotients without Using the Quotient Rule

23. 11.4 The Product Rule and the Quotient Rule ( 5 of 6 )

24. 11.4 The Product Rule and the Quotient Rule ( 6 of 6 ) Example 9 – Finding Marginal Propensities to Consume and to Save

25. Home Work If a manufacturer's average-cost equation is Find the marginal-cost function. What is the marginal cost when 15 units are produced? If the demand equation for a manufacturer's product is where p denotes the price per unit for q units. Find the marginal-revenue function in each case. ( Recall that revenue = p.q )

26. Haeussler , Jr. E.F., Paul, R. S., Wood, R. J. (2019). Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences . 14th. Ontario: Pearson. References