1. Home
  2. Flashcards
  3. Preview

Calc 1 review

  1. ∫ cot(x) dx =
    = ln(|sin(x)|) + C
  2. ∫1/cos2(x) dx=
    = tan(x) +C
  3. d/dx [f(x)/g(x)]=
    • =  [f'(x)g(x)-g'(x)f(x)]
    •     ----------------------
    •             (g(x))2
  4. logarithmic rule
    logbMN=
    =logbM +logbN
  5. logarithmic rule
    logb(M/N)=
    =logbM-logbN
  6. logarithmic rule
    logbMp =
    =P(logbM)
  7. d/dx[sin-1 u]=
    • =     1
    •   ---------- (du/dx)
    •    √(1-u2)
  8. d/dx [csc-1 u] =
    • =      -1
    •    ------------  (du/dx)
    •    |u|√(u2-1)
  9. d/dx[cos(x)]=
    = -sin(x)
  10. d/dx[tan(x)]=
    = sec2(x)
  11. ∫1/x dx=
    = ∫x-1 dx

    = ln(|x|) + C
  12. ∫[f(x)+g(x)] dx =
    = ∫f(x) dx + ∫g(x) dx
  13. ∫[f(x) -g(x)] =
    =∫f(x) dx - ∫g(x) dx
  14. d/dx [sin(u)] =
    = cos(u) * du/dx
  15. d/dx [cos(u)]=
    = -sin(u) * du/dx
  16. d/dx [eu]=
    =eu * du/dx
  17. ∫ax dx =
    =(ax)/(ln(a)) +C
  18. ∫sec2(x) dx =
    =∫1/(cos2(x)) dx

    =tan(x) +C
  19. d/dx [c]=
    = 0
  20. d/dx [csc(x)]=
    = -csc(x)cot(x)
  21. d/dx (x) =
    1
  22. d/dx (ex)=
    =ex
  23. d/dx (bx)=
    = bxln(b)
  24. d/dx[sin(x)]=
    =cos(x)
  25. d/dx [ln(x)]=
    =1/x

    x>0
  26. d/dx [ln(u)]=
    =1/u * (du/dx)

    x>0
  27. d/dx [cos(u)]=
    = -sin(u) * du/dx
  28. d/dx [eu]=
    = eu * du/dx
  29. ∫ax dx=
    =(ax)/ln(a) +C
  30. ∫sec2(x)dx=
    =∫1/cos2(x) dx

    =tan(x)+C
  31. d/dx [sec-1(u)]=
    • =         1
    •    --------------  * (du/dx)
    •    |u|√(u2 +1)
  32. d/dx [tan-1(u)]=
    • =     1
    •    --------- * (du/dx)
    •      u2 +1
  33. d/dx [c f(x)]=
    =cf'(x)
  34. du/dx [u(x)]n=
    =n[u(x)]n-1 * u'(x)

    or

    =nun-1 *du/dx
  35. d/dx [csc(u)]=
    = -csc(u)cot(u) *du/dx
  36. d/dx [tan(u)]=
    =sec2(u) * du/dx
  37. d/dx [sec(u)]=
    =sec(u)tan(u) * du/dx
  38. ∫tan(x) dx =
    = ln|sec(x)| +C

    or

    = -ln|cos(x)|+C
  39. d/dx[sec(x)]=
    sec(x)tan(x)
  40. d/dx (xn)=
    =n(xn-1)
  41. d/dx[cot(x)]=
    = -csc2(x)
  42. ∫cot(x) dx=
    = ln|sin(x)| + C
  43. ∫sec(x) dx =
    = ln|sec(x)+tan(x)| + C
  44. d/dx[f(x)±g(x)]=
    = f'(x) ± g'(x)
  45. d/dx [f(g(x))]=
    = f'(g(x))*g'(x)
  46. d/dx [sec(x)]=
    = sec(x)tan(x)
  47. d/dx [cot(x)]=
    = -csc2(x)
  48. d/dx [logax]=
    = 1/(x*ln(a))
  49. d/dx logau =
    = 1/u*ln(a) * du/dx
  50. ∫csc2(x) dx =
    = -cot(x)+C
  51. ∫1/(√1-x2) dx =
    =sin-1(x) +C
  52. ∫sec2(x) dx =
    = tan(x) +C
  53. ∫cot2(x) dx=
    = -cot(x) - x + C
Author
saucyocelot
ID
358563
Card Set
Calc 1 review
Description
Review: derivatives and integration
Updated

  1. Home
  2. Flashcards
  3. Preview