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Text File  |  1989-10-26  |  4KB  |  113 lines
  1.  
  2.                          Review of Differentiation
  3.                          ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
  4.     
  5.        List of standard derivatives.
  6.  
  7.                              d
  8.                              ──  c     =   O  
  9.                              dx      
  10.  
  11.                              d    n           n - 1
  12.                              ──  x     =   n x
  13.                              dx      
  14.  
  15.                              d    x         x
  16.                              ──  e     =   e
  17.                              dx      
  18.  
  19.                              d              1
  20.                              ──  ln x  =   ───
  21.                              dx             x
  22.  
  23.                             d
  24.                             ──  sin x  =   cos x
  25.                             dx      
  26.  
  27.                             d
  28.                             ──  cos x  =   -sin x
  29.                             dx      
  30.  
  31.                             d                 2
  32.                             ──  tan x  =   sec x
  33.                             dx      
  34.  
  35.                             d                  2
  36.                             ──  cot x  =   -csc x
  37.                             dx      
  38.  
  39.                             d
  40.                             ──  sec x  =   sec x tan x
  41.                             dx      
  42.  
  43.                             d
  44.                             ──  csc x  =   -csc x cot x
  45.                             dx      
  46.  
  47.                            d      -1            1
  48.                            ──  sin  x  =   ───────────
  49.                            dx                    2 1/2
  50.                                            (1 - x )
  51.  
  52.                            d      -1          1
  53.                            ──  tan  x  =   ────────
  54.                            dx                    2
  55.                                             1 + x 
  56.  
  57.  
  58.  
  59.  
  60.        List of standard theorems
  61.  
  62.                     d                     d           d
  63.                     ── ( f(x) ± g(x) ) =  ── f(x)  ±  ── g(x)
  64.                     dx                    dx          dx
  65.  
  66.  
  67.                       d                   d                    d
  68.                       ── ( f(x) g(x) ) =  ── f(x) g(x) +  f(x) ── g(x)
  69.                       dx                  dx                   dx
  70.  
  71.  
  72.  
  73.                                            d                   d
  74.                                            ── f(x) g(x) - f(x) ── g(x)
  75.                          d    f(x)         dx                  dx
  76.                          ──  ──────    =  ──────────────────────────────
  77.                          dx   g(x)                      2
  78.                                                        g (x)
  79.  
  80.  
  81.                            x
  82.                       d   ⌠
  83.                       ──  │  f(t) dt   =   f(x)
  84.                       dx  ⌡
  85.                            a
  86.  
  87.                                                  dy     dy  du
  88. Chain Rule:  If y = f(u) and u = g(x) then       ──  =  ──  ──
  89.                                                  dx     du  dx
  90.  
  91.  
  92. ┌─────────────────┐
  93. │ Common Mistakes │
  94. └─────────────────┘
  95.  
  96. Perhaps the most common mistake is a sign error when differentiating the
  97. trig functions.
  98.  
  99.  
  100.                    d                    d         d
  101. WRONG              ── f(x) g(x)    =    ── f(x)   ── g(x)
  102.                    dx                   dx        dx
  103.  
  104.  
  105.  
  106.                  d                    d           d
  107. WRONG            ── f(x) ÷ g(x)    =  ── f(x)  ÷  ── g(x)
  108.                  dx                   dx          dx
  109.  
  110.  
  111. This is the end of the help file.  Press the ESC key to return to the quiz
  112. question you were doing.
  113.