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200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Limit Definition of Derivatives Basic Rules Product,

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Presentation on theme: "200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Limit Definition of Derivatives Basic Rules Product,"— Presentation transcript:

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2 Limit Definition of Derivatives Basic Rules Product, Quotient, and Higher Order Derivatives Chain Rule Implicit Differentiation Final Jeopardy

3 Main Get Answer Limit Definition of Derivatives 100 Use the limit definition for derivatives to find the derivative of.

4 Main Limit Definition of Derivatives 100 If,

5 Main Get Answer Limit Definition of Derivatives 200 Use the limit definition for derivatives to find the derivative of at x = 4.

6 Main Limit Definition of Derivatives 200 If,

7 Main Get Answer Limit Definition of Derivatives 300 Find the equation of the tangent line to at x = -3 by using the limit definition of derivatives.

8 Main Limit Definition of Derivatives 300 If, Equation of Tangent Line at x = -3:

9 Main Get Answer Limit Definition of Derivatives 400

10 Main Limit Definition of Derivatives 400 if.

11 Main Get Answer Limit Definition of Derivatives 500 If f (x) is continuous and differentiable at x = 1. Find a and b.

12 Main Limit Definition of Derivatives 500 If, If f (x) is continuous and differentiable at x = 1. and.

13 Main Get Answer Basic Rules 100 Which of the following might be the graph of ? a) b) c) d) e)

14 Main Basic Rules 100 c)

15 Main Get Answer Basic Rules 200

16 Main Basic Rules 200

17 Main Get Answer Basic Rules 300 Find the tangent line of at (2,16).

18 Main Basic Rules 300 If,  At (2,16),. Equation of Tangent Line at x = 2:

19 Main Get Answer Basic Rules 400 Find the tangent line of at  MAY USE CALCULATOR

20 Main Basic Rules 400 Main If,  and  Equation of Tangent Line at x = -3:

21 Main Get Answer Basic Rules 500 Find the equation of the line perpendicular to the tangent line of at.

22 Main Basic Rules 500 Main If,   and  Equation of Tangent Line at x = 1:

23 Product, Quotient, and Higher Order Derivatives 100 Main Get Answer If, find.

24 Product, Quotient, and Higher Order Derivatives 100 Main If,

25 Product, Quotient, and Higher Order Derivatives 200 Main Get Answer

26 Product, Quotient, and Higher Order Derivatives 200 Main

27 Product, Quotient, and Higher Order Derivatives 300 Main Get Answer Find f ’(x) in its simplest form.

28 Product, Quotient, and Higher Order Derivatives 300 Main Find f ’(x) in its simplest form

29 Product, Quotient, and Higher Order Derivatives 400 Main Get Answer The position of a particle is given by: What is the acceleration of the particle at: Use a calculator!

30 Product, Quotient, and Higher Order Derivatives 400 Main The position of a particle is given by: What is the acceleration of the particle at: Use a calculator!

31 Product, Quotient, and Higher Order Derivatives 500 Main Get Answer Find do NOT use a CALCULATOR!

32 Product, Quotient, and Higher Order Derivatives 500 Main

33 Get Answer Chain Rule 100 Let f and u be differentiable functions of x. Find

34 Main Chain Rule 100 Let f and u be differentiable functions of x.

35 Main Get Answer Chain Rule 200 Differentiate.

36 Main Chain Rule 200 Differentiate.,.

37 Main Get Answer Chain Rule 300 Differentiate.

38 Main Chain Rule 300 Differentiate.

39 MainGet Answer Chain Rule 400 Find the exact answer AND the decimal answer. Use a calculator. Find if.

40 Main Chain Rule 400

41 MainGet Answer Chain Rule 500 Suppose that functions f and g have the following values. What is the value of the derivative of at ?

42 Main Chain Rule 500 Suppose that functions f and g have the following values. What is the value of the derivative of at ?

43 MainGet Answer Implicit Differentiation 100 Find :

44 Main Implicit Differentiation 100 Find :

45 Main Get Answer Implicit Differentiation 200 Find :

46 Main Implicit Differentiation 200 Find :

47 Main Get Answer Implicit Differentiation 300 Find in its simplest form.

48 Main Implicit Differentiation 300 Find in its simplest form.

49 Main Get Answer Implicit Differentiation 400 Find the slope of the tangent line when x = 1 and y = 3.

50 Main Implicit Differentiation 400 Find the slope of the tangent line when x = 1 and y = 3.

51 Main Get Answer Implicit Differentiation 500 Find the slope of the tangent line when x = 2.

52 Main Implicit Differentiation 500 Find the slope of the tangent line when x = 2.

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54 A Patrol Car is parked 50 feet from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall (in ft/sec) when the beam makes an angle of ?

55 A Patrol Car is parked 50 feet from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall (in ft/sec) when the beam makes an angle of ? Remember:


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