1. Some of the material in these slides is from Calculus 9/E by
Review of Derivatives
Some of the material in these slides is from Calculus 9/E by
Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.

2. Derivative = Slope of Tangent Line

3. Derivative = Slope of Tangent Line
Definition (p. 132)‏

4. Alternate Derivative Formulations

5. Alternate Derivative Formulations – Independent Time Variable

6. Derivative Function Definition
Definition (p. 143)‏

7. Differentiability
Definition (p. 146)‏

8. Theorem 2.3.2 (p. 156) The Power Rule
Derivative Rules
Theorem (p. 156) The Power Rule

9. Theorem 2.3.3 (p. 157) Extended Power Rule
Derivative Rules
Derivative Rules
Theorem (p. 157) Extended Power Rule

10. Theorem 2.3.4 (p. 157) Constant Multiple Rule
Derivative Rules
Theorem (p. 157) Constant Multiple Rule

11. Theorem 2.3.5 (p. 158) Sum and Difference Rules
Derivative Rules
Theorem (p. 158) Sum and Difference Rules

12. Theorem 2.4.1 (p. 164) The Product Rule
Derivative Rules
Theorem (p. 164) The Product Rule

13. Theorem 2.4.2 (p. 165) The Quotient Rule
Derivative Rules
Theorem (p. 165) The Quotient Rule

14. Derivative Rules

15. Derivatives of Trig Functions
Formula (3) (p. 169)‏
Formula (4)‏

16. Derivatives of Trig Functions
Formula (5) (p. 170)‏
Formula (6)‏
Formula (7)‏
Formula (8)‏

17. Theorem 2.6.1 (p. 174) The Chain Rule
Derivatives of Composite Functions – Chain Rule
Theorem (p. 174) The Chain Rule

18. Derivatives of Logarithmic Functions
Equations (p. 193)‏

19. Derivatives of Exponential Functions
Equations (p. 199)‏

20. Derivatives of Inverse Trig Functions
Equations (p. 201)‏

21. Implicit Differentiation
Find dy/dx by implicit differentiation:

22. Select the best answer for the following question.
During the first 50 seconds of a missile launch, the missile is propelled straight up so that in t seconds, it reaches a height of feet. What is the average velocity of the missile during the first 50 seconds?
12,500 ft/sec
1,500 ft/sec
38,250 ft/sec
75,000 ft/sec
Question 1

23. Select the best answer for the following question.
2. Find if
Question 2

24. Select the best answer for the following question.
3. Which of the following equations has derivative
Question 3

25. Select the best answer for the following question.
4. For , find f '(x)
Question 4

26. Select the best answer for the following question.
5. For , find y’ .
Question 6

27. Select the best answer for the following question.
6. For , find
Question 7

28. Answers
1.b 5. a
2.c 6. d
3.a
4.b