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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 f(x)=cosx is?
-csc^2x
-sinx
v2/2
1/2

2. When do derivatives not exist?
-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
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2

3. Deriv of e^x
v3/2
-1
0
e^x

4. sin 7p/4
sec^2x
-v2/2
-v3/2
1

5. sin 11p/6
v3/3
v3/2
-1/2
-csc^2x

6. cos 2p/3
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
-1/2
1
-v3/2

7. tan 7p/6
0
v3/3
1/(u ln a ) du/dx
v3/2

8. Deriv of csc^(-1)x
0
-1/(|x| v(x^2-1))
1/2
v2/2

9. What is the product rule?
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2
1
1

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

11. tan p/4
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v2/2
1
-v3/3

12. sin p/4
v2/2
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
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

13. tan 2p
0
v3/3
-1/2
slope of the tangent line

14. tan 5p/6
1
v2/2
-v3/3
-1

15. cos p/2
0
v3/2
-v3/2
v3/2

16. sin 7p/6
1/2
1/2
v3/2
-1/2

17. cos 5p/3
v3
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
-v3/2

18. cos 5p/4
-1
1/2
-v2/2
-cscxcotx

19. Explicit differentiation
1
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
-1/2

20. tan p/6
-v3/2
v3/2
v3/3
v2/2

21. tan 11p/6
0
-v3/3
1/2
1/v(1-x^2 )

22. Deriv of tan^(-1)x
undefined
-1/2
1/(1+x^2 )
a^u lna du/dx

23. sin p/2
e^x
-csc^2x
1
1/2

24. Deriv of sin^(-1)x
-v3/3
-v3/2
1/v(1-x^2 )
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

25. sin p/3
0
v3/2
0
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value

26. cos 5p/6
-csc^2x
-v3/2
v2/2
undefined

27. derivative
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/v(1-x^2 )
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
slope of the tangent line

28. Deriv of sec^(-1)x
0
v3/2
1/(|x| v(x^2-1))
1/2

29. cos 11p/6
tanxsecx
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v2/2

30. Deriv of f(x)=sinx is?
0
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
cosx
1

31. sin 5p/4
tanxsecx
-v3
-v2/2
-1/(|x| v(x^2-1))

32. Deriv of a^u
1/u du/dx
a^u lna du/dx
0
1/(1+x^2 )

33. Implicit differentiation
-1/2
v3/3
1/v(1-x^2 )
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

34. sin 2p/3
-v3/3
v3/2
-cscxcotx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

35. What is the Chain Rule? When can it be used?
1/2
1/(u ln a ) du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
a^u lna du/dx

36. sin 3p/2
-1
-v3/3
-1/2
-sinx

37. What is the Alternate definition of a derivative and what does it find?
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value
0
-v3/2
v3/3

38. tan p/3
cosx
undefined
v3
-v3/2

39. Deriv of f(x)=csc is?
-cscxcotx
v3/2
1/(1+x^2 )
v3/2

40. Deriv of f(x)=cotx is?
1/(u ln a ) du/dx
-csc^2x
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

41. tan 3p/4
v3
-1
tanxsecx
-v2/2

42. cos p/6
undefined
-1
-v3/2
v3/2

43. tan 2p/3
v3/2
0
-v2/2
-v3

44. tan p/2
undefined
-v3/2
v3
-1

45. sin 5p/3
sec^2x
-v3/2
1/(|x| v(x^2-1))
1/v(1-x^2 )

46. cos 2p
-cscxcotx
1
slope of the tangent line
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

47. Deriv of ln u
v2/2
1/u du/dx
1
1/(|x| v(x^2-1))

48. sin 3p/4
0
v2/2
-1/2
1/(u ln a ) du/dx

49. cos 3p/4
-v2/2
1/v(1-x^2 )
1/(|x| v(x^2-1))
-sinx

50. Deriv of f(x)=tanx is?
1/(|x| v(x^2-1))
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
sec^2x
-1

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