
                         Review of Differentiation
                         ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
    
       List of standard derivatives.

                             d
                             ──  c     =   O  
                             dx      

                             d    n           n - 1
                             ──  x     =   n x
                             dx      

                             d    x         x
                             ──  e     =   e
                             dx      

                             d              1
                             ──  ln x  =   ───
                             dx             x

                            d
                            ──  sin x  =   cos x
                            dx      

                            d
                            ──  cos x  =   -sin x
                            dx      

                            d                 2
                            ──  tan x  =   sec x
                            dx      

                            d                  2
                            ──  cot x  =   -csc x
                            dx      

                            d
                            ──  sec x  =   sec x tan x
                            dx      

                            d
                            ──  csc x  =   -csc x cot x
                            dx      

                           d      -1            1
                           ──  sin  x  =   ───────────
                           dx                    2 1/2
                                           (1 - x )

                           d      -1          1
                           ──  tan  x  =   ────────
                           dx                    2
                                            1 + x 




       List of standard theorems

                    d                     d           d
                    ── ( f(x) ± g(x) ) =  ── f(x)  ±  ── g(x)
                    dx                    dx          dx


                      d                   d                    d
                      ── ( f(x) g(x) ) =  ── f(x) g(x) +  f(x) ── g(x)
                      dx                  dx                   dx



                                           d                   d
                                           ── f(x) g(x) - f(x) ── g(x)
                         d    f(x)         dx                  dx
                         ──  ──────    =  ──────────────────────────────
                         dx   g(x)                      2
                                                       g (x)


                           x
                      d   ⌠
                      ──  │  f(t) dt   =   f(x)
                      dx  ⌡
                           a

                                                 dy     dy  du
Chain Rule:  If y = f(u) and u = g(x) then       ──  =  ──  ──
                                                 dx     du  dx


┌─────────────────┐
│ Common Mistakes │
└─────────────────┘

Perhaps the most common mistake is a sign error when differentiating the
trig functions.


                   d                    d         d
WRONG              ── f(x) g(x)    =    ── f(x)   ── g(x)
                   dx                   dx        dx



                 d                    d           d
WRONG            ── f(x) ÷ g(x)    =  ── f(x)  ÷  ── g(x)
                 dx                   dx          dx


This is the end of the help file.  Press the ESC key to return to the quiz
question you were doing.
