home
***
CD-ROM
|
disk
|
FTP
|
other
***
search
/
Hall of Fame
/
HallofFameCDROM.cdr
/
tutor
/
rurc3.lzh
/
CIII_3.HLP
< prev
next >
Wrap
Text File
|
1989-10-26
|
4KB
|
113 lines
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.