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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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)=sinx is?
f(x) = (u)(v) AND f'(x) = u'v + v'u
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
cosx
1/2

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

3. Deriv of e^x
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
e^x
1/2

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

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

6. tan 7p/4
-1
slope of the tangent line
e^x
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

7. sin 5p/4
-v2/2
-1/2
-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

8. Deriv of f(x)=secx is?
-1
v3
tanxsecx
v3/3

9. derivative
sec^2x
slope of the tangent line
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
1/2

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

11. cos p/2
-v2/2
-sinx
0
-v2/2

12. cos p/6
-v2/2
1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2

13. tan 7p/6
-cscxcotx
v3/3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1

14. cos 7p/4
v3/3
v2/2
1/2
1/v(1-x^2 )

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

16. cos 5p/4
v3/2
-v2/2
1/2
-cscxcotx

17. sin 2p
v3/2
0
1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

18. tan 3p/2
-cscxcotx
-v2/2
-v3/2
undefined

19. Deriv of f(x)=csc is?
-cscxcotx
-v3/3
0
-v3

20. Deriv of ln u
-v3/2
-1
sec^2x
1/u du/dx

21. cos 5p/3
-1
1/2
-1/(|x| v(x^2-1))
v2/2

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

23. Implicit differentiation
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
0
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-sinx

24. cos 11p/6
-v3/3
-v3/3
v3/2
-v3/2

25. sin 7p/4
-1/2
sec^2x
v3/3
-v2/2

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

27. sin p
sec^2x
e^x
0
-1/(|x| v(x^2-1))

28. tan p/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
1
-v2/2
1/2

29. tan 5p/6
-v3/3
-v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/(1+x^2 )

30. cos 4p/3
1
v3/3
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

31. Deriv of f(x)=tanx is?
undefined
sec^2x
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

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

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

34. cos 5p/6
-v3/2
-1/(|x| v(x^2-1))
v2/2
-cscxcotx

35. sin 3p/4
1/(u ln a ) du/dx
v2/2
-cscxcotx
a^u lna du/dx

36. Deriv of cot^(-1)x
-1/(1+x^2 )
1/(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
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

37. sin p/3
-v2/2
-sinx
v3/2
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

38. tan 2p/3
v3/2
-v3
-1
1/(u ln a ) du/dx

39. What is the Alternate definition of a derivative and what does it find?

40. Deriv of tan^(-1)x
-v2/2
v3
1/(1+x^2 )
-cscxcotx

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

42. sin p/6
0
1/2
v3/2
tanxsecx

43. What is the quotient rule?

44. sin 7p/6
f(x) = (u)(v) AND f'(x) = u'v + v'u
a^u lna du/dx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/2

45. tan 3p/4
-v3/2
e^x
-1
sec^2x

46. sin 2p/3
1
1/2
v3/2
-1/2

47. tan 5p/3
v2/2
-sinx
1/v(1-x^2 )
-v3

48. sin 5p/6
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v2/2
1/2

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

50. sin p/4
v3/2
v2/2
v3
1/(1+x^2 )