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.

Derivative = Slope of Tangent Line

Derivative = Slope of Tangent Line Definition 2.1.1 (p. 132)‏

Alternate Derivative Formulations

Alternate Derivative Formulations – Independent Time Variable

Derivative Function Definition Definition 2.2.1 (p. 143)‏

Differentiability Definition 2.2.2 (p. 146)‏

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

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

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

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

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

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

Derivative Rules

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

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

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

Derivatives of Logarithmic Functions Equations 2 - 5 (p. 193)‏

Derivatives of Exponential Functions Equations 5 - 8 (p. 199)‏

Derivatives of Inverse Trig Functions Equations 9 - 11 (p. 201)‏

Implicit Differentiation Find dy/dx by implicit differentiation:

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

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

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

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

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

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

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