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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. Explicit differentiation
1/(u ln a ) du/dx
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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v3/2

2. Deriv of sin^(-1)x
a^u lna du/dx
1/v(1-x^2 )
0
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

3. tan 5p/6
-v3/3
1/u du/dx
undefined
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

4. tan 7p/6
1/(|x| v(x^2-1))
1/u du/dx
-v2/2
v3/3

5. Deriv of f(x)=cotx is?
-csc^2x
1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1

6. tan 5p/4
-v3
1
v2/2
1/(1+x^2 )

7. cos 11p/6
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3/2
v2/2
1/(u ln a ) du/dx

8. cos p/4
v2/2
slope of the tangent line
-v2/2
-v2/2

9. cos 7p/4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
0
-1

10. Deriv of e^x
0
-v3/2
1/(u ln a ) du/dx
e^x

11. sin 5p/3
-v3/2
-v2/2
-1/v(1-x^2 )
0

12. tan 4p/3
v3
v3/2
1/(u ln a ) du/dx
v2/2

13. cos 5p/3
v3
1/2
-v3/2
e^x

14. When do derivatives not exist?
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
1
1
-v3/2

15. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
-1/2
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

16. Guidelines for implicit differentiation
-v3/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
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

17. What is the Alternate definition of a derivative and what does it find?
v2/2
-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
undefined

18. tan p/6
v3/3
-1/(|x| v(x^2-1))
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/(u ln a ) du/dx

19. tan 2p
-1/2
0
-1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

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

21. cos 2p/3
v3/2
-csc^2x
-v2/2
-1/2

22. sin 4p/3
-v2/2
1
-v3/2
1

23. cos p/3
-1
-v3
1/2
v3/2

24. cos 3p/4
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
-v2/2
cosx
1

25. tan 7p/4
tanxsecx
-1
-v3/2
1/2

26. tan 3p/4
0
1/(|x| v(x^2-1))
-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

27. sin 3p/2
-v2/2
v2/2
1
-1

28. Deriv of a^u
0
-1/(1+x^2 )
v3/2
a^u lna du/dx

29. tan 11p/6
-v3/3
-1/(|x| v(x^2-1))
1
v2/2

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

31. Implicit differentiation
-1
0
-1/(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

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

33. sin 5p/4
v3
-v2/2
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
v2/2

34. cos p/2
-1/2
v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
0

35. tan p
slope of the tangent line
tanxsecx
1
0

36. sin 2p/3
1/u du/dx
1
v3/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

37. sin 11p/6
v3
-v2/2
a^u lna du/dx
-1/2

38. tan p/4
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
-v2/2
-1/2

39. tan 3p/2
v3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
undefined
-1

40. Deriv of f(x)=sinx is?
cosx
-v2/2
-1
tanxsecx

41. sin p
-v2/2
0
undefined
1/u du/dx

42. Deriv of ln u
1/2
-v2/2
1/u du/dx
-1

43. What is the quotient rule?
-1/2
v3/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
0

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

45. cos p
-v3/2
-1
0
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

46. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1
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
-v3/2

47. sin 7p/6
slope of the tangent line
1/u du/dx
-1/2
1

48. sin 3p/4
1
e^x
v2/2
0

49. Deriv of f(x)=csc is?
slope of the tangent line
-1/(1+x^2 )
1
-cscxcotx

50. cos 7p/6
1/2
-v3/2
-v3/3
-cscxcotx

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