2. THIS IS
Calc Jeopardy!!!

3. WITH YOUR
HOST…
Erika Jaeger

4. Jeopardy
Name that Rule!
Implicit diff.
Log Rules!
Derivative
Random
100
100
100
100
100
200
200
200
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200
300
300
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400
400
400
400
500
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500
500

5. Name this rule…
y = c
y’= 0
A 100

6. What is the constant rule?

7. Name this rule…
y = Xn
y’= n(x)n-1
A 200

8. What is the power rule?
A 200

9. This rule is used to take the derivative of fractions
This rule is used to take the derivative of fractions. (state the name and equation)
A 300

10. y’ = (LoDHi – HiDLo)/(Lo)2
What is Quotient Rule?
y = Hi/Lo
y’ = (LoDHi – HiDLo)/(Lo)2
A 300

11. This is the correct way to take the derivative of the following function. (if false, provide correct answer)
y = 3e(12x+1/x)
y’ = 3(12x+1/x)e(12x+1/x)^-1
A 400

12. What is False?
y = 3e(12x+1/x)
y’ = (36 – 3/x2) e(12x+1/x)
A 400

13. What rules do I use to solve the following?
y = Sin(x2+x+1) – 1/x
A 500

14. What is …
Constant Multiple Rule, Sum/Difference Rule, Chain Rule, and Power Rule?
A 500

15. The 2nd derivative of
y = 3x3+2x2+x+1.
B 100

16. What is
y’’ = 18x+4?
B 100

17. The derivative of
y = 1/x2 + 4/x + x +20.
B 200

18. What is
y’ = -2/x3 - 4/x2 + 1 ?
B 200

19. The derivative of
y = (e2x+3+x)(x3)
B 300

20. (e2x+3+x)(3x2)+(x3)(2e2x+3+1)
What is
y’ =
(e2x+3+x)(3x2)+(x3)(2e2x+3+1)
= 3x2e2x+3+3x3+2x3e2x+3+x3
= x2(3e2x+3+3x+2xe2x+3+x)
= x2(3e2x+3+2xe2x+3+4x)
B 300

21. The derivative of
y = (1/x -3)(3/x+9)
B 400

22. What is
y’ = -6/x3 ?
B 400

23. The derivative of
f(x) = 1/(1+Cot2x).
B 500

24. What is
f’(x) = 2(Sinx)*Cosx ?
B 500

25. True or false: The quotient rule is y = f(x)/g(x)
y’ = f(x)g’(x) – g(x)f’(x)
g2(x)
C 100

26. y’ = g(x)f’(x) – f(x)g’(x)
What is False?
y’ = g(x)f’(x) – f(x)g’(x)
g2(x)
C 100

27. The velocity and speed of the following function at t = Π/4 is…
s = 1-3Sin(t)
C 200

28. What is
s’ = -3Cos(Π/4) = -3rt(2)/2
Speed = 3rt(2)/2
C 200

29. This was John Locke’s predominant power, because it is the most active power

30. What is Legislative Power?
C 300

31. DAILY DOUBLE
DAILY DOUBLE
C 400

32. The name of the first, second, and third derivative

33. What is velocity, acceleration, and jerk?

34. There is no derivative if there is a…
*hint: there are multiple answers
C 500

35. What is a corner, cusp, vertical tangent, or discontinuity?

36. The 3 steps to implicitly differentiate are…

37. Step 1: Differentiate both sides
What is
Step 1: Differentiate both sides
Step 2: Collect all dy/dx
Step 3: Solve for dy/dx
D 100

38. The derivative of x2 +y2 = 9 .
D 200

39. What is dy/dx= -x/y ?
D 200

40. The derivative of
2y =x2+Sin(y).
D 300

41. What is
dy/dx= (2x)/(2-Cos(y)) ?
D 300

42. The derivative of
8x2y + 7xy2 = -7
D 400

43. What is
(-16xy-7y2)/(8x2+14xy) ?
D 400

44. The derivative, slope, and equation of the tangent line to
x2/4 + y2/16 = 1
at point (1, 2rt(3))
D 500

45. What is
dy/dx = -4x/y
m = -2/rt(3)
y = [-2/rt(3)]x + 8/rt(3)
D 500

46. The rule to split the following function up is
y = ln(AB)
E 100

47. What is y = ln(A)+ln(B)?
E 100

48. The rule to split up the following function is
y = ln(a/b)
E 200

49. What is y = ln(a) – ln(b)?
E 200

50. logb(mn) can be expanded to look like…

51. What is n · logb(m)
E 300

52. Logarithmic Differentiation
The Final Jeopardy Category is:
Logarithmic Differentiation
Please record your wager.
Click on screen to begin

53. Use Logarithmic differentiation to solve y = (x+3)/(x+1)
Final Question:
Use Logarithmic differentiation to solve
y = (x+3)/(x+1)
Click on screen to continue

54. Click on screen to continue
Final Answer:
What is
dy/dx = -2/(x+1)2
Work:
Ln both sides
lny = ln[(x+3)/(x+1)]
lny = ln(x+3) – ln(x+1)
Differentiate
1/y *dy/dx = 1/(x+3) – 1/(x+1)
find common denominator
dy/dx = [-2/(x+3)(x+1)]*y
replace y.
dy/dx = [-2/(x+3)(x+1)]*[(x+3)/(x+1)]
dy/dx = -2/(x+1)(x+1)
dy/dx = -2/(x+1)2
Click on screen to continue

55. Thank You for Playing
CALC JEOPARDY