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2.2 Basic Differentiation Rules and Rate of Change

2.2 Basic Differentiation Rules and Rate of Change. Using the constant rule. Using the power rule. Finding the slope of the graph. Find the slope of the graph of when: x=-1 x=0 x=1. Finding an Equation of a Tangent Line.

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2.2 Basic Differentiation Rules and Rate of Change

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  1. 2.2 Basic Differentiation Rules and Rate of Change

  2. Using the constant rule

  3. Using the power rule

  4. Finding the slope of the graph • Find the slope of the graph of when: • x=-1 • x=0 • x=1

  5. Finding an Equation of a Tangent Line • Find an equation of the tangent line to the graph of f(x) when x=-2.

  6. Using the Constant Multiple Rule

  7. More Using Constant Multiple Rule

  8. Using Parentheses When Differentiating

  9. More Using Parentheses When Differentiating

  10. Using Sum and Difference Rules

  11. Derivatives of Sine and Cosine Functions

  12. Derivatives Involving Sine and Cosine

  13. Rates of Change • Average Velocity Change in Distance Change in Time

  14. Finding Average Velocity of a Falling Object • If a billiard ball is dropped from a height of 100 ft, its height s at time t is given by where s is measured in feet and t is measured in seconds. Find the average velocity over each of the following time intervals. a. [1.2] b. [1,1.5] c. [1,1.1]

  15. Instantaneous Velocity Position Function So is the initial height of the object, vo is the initial velocity of the object, and g is the acceleration due to gravity. On Earth, the value of g is approximately -32 feet per second or -9.8 meters per second.

  16. Using Derivative to Find Velocity • At time t=0, a diver jumps from a platform diving board that is 32 feet above the water. The position of the diver is given by where s is measured in feet and t is measured in seconds. a. When does the diver hit the water? b. What is the diver’s velocity at impact?

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