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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Deriv of tan^(-1)x
a^u lna du/dx
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
1/(1+x^2 )
v2/2

2. cos 3p/2
v3/2
v2/2
0
-v3

3. sin 2p
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
-cscxcotx
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

4. Deriv of log_au=
v3/2
-v3
0
1/(u ln a ) du/dx

5. cos p
undefined
-1
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
1/(u ln a ) du/dx

6. Implicit differentiation
1/2
1
-1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

7. What is the product rule?

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8. tan 2p/3
1
-v3
v3/3
0

9. tan p
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
sec^2x
1
0

10. sin p/2
1/(|x| v(x^2-1))
1
cosx
v3/2

11. cos 5p/4
1/2
1/(|x| v(x^2-1))
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v2/2

12. Deriv of f(x)=csc is?
v3/2
v3
-cscxcotx
-sinx

13. Deriv of sin^(-1)x
tanxsecx
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5
-1/2
1/v(1-x^2 )

14. tan 3p/4
1/u du/dx
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1

15. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-sinx
v2/2
-1/(1+x^2 )

16. Guidelines for implicit differentiation
v2/2
1
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
-cscxcotx

17. cos 4p/3
-v3/2
v2/2
-1/2
1

18. sin 11p/6
-1/2
-1/v(1-x^2 )
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

19. tan p/2
-v2/2
-v2/2
undefined
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5

20. cos 2p/3
0
1/2
-1/2
0

21. Deriv of f(x)=tanx is?
1
sec^2x
1
cosx

22. derivative
-v3/3
slope of the tangent line
1/2
v2/2

23. tan 11p/6
1
-1/2
1/v(1-x^2 )
-v3/3

24. sin p/3
v3/2
-v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
0

25. sin 4p/3
-1/v(1-x^2 )
-v3/2
-1
-1

26. tan p/6
v3/2
v3/3
v3/2
-1

27. sin p/4
-v3/3
v2/2
v3/2
v3/2

28. sin 3p/2
undefined
v3/2
-1
a^u lna du/dx

29. tan 2p
-v2/2
v3
0
-1/2

30. cos 7p/6
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/2
cosx
-1

31. When do derivatives not exist?
-1/2
1/2
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
-v2/2

32. tan 5p/6
1/2
-v3/2
-v3/3
-v3/2

33. Deriv of a^u
v3/2
a^u lna du/dx
-v3
slope of the tangent line

34. tan 7p/4
0
-1
1/(1+x^2 )
-1/2

35. Deriv of f(x)=sinx is?
-v3/2
v2/2
cosx
0

36. sin 5p/6
-v2/2
sec^2x
1/2
a^u lna du/dx

37. Deriv of f(x)=cotx is?
-v3/3
v3/3
-csc^2x
f(x) = (u)(v) AND f'(x) = u'v + v'u

38. sin 2p/3
-1/(|x| v(x^2-1))
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2

39. cos 11p/6
-1/2
-1
v3/2
1

40. What is the quotient rule?

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41. what is the the limit definition of a derivative and what does it find?

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42. tan p/4
sec^2x
-v2/2
1
v2/2

43. sin p
0
v2/2
v2/2
v3

44. sin 3p/4
-v2/2
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2

45. sin 7p/6
v2/2
v3/3
-sinx
-1/2

46. tan 4p/3
-1
-v2/2
-1/(|x| v(x^2-1))
v3

47. sin 5p/4
-v3
-v2/2
v2/2
-1/2

48. Deriv of cos^(-1)x
-1/v(1-x^2 )
v3/2
undefined
cosx

49. tan 5p/3
0
-v2/2
-v3
v3/2

50. Explicit differentiation
undefined
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5
0
v2/2