MATH
Kamis, 31 Maret 2011
Table of Derivatives
Power of x.
c = 0
x = 1
x
n
= n x
(n-1)
Proof
Exponential / Logarithmic
e
x
= e
x
Proof
b
x
= b
x
ln(b)
Proof
ln(x) = 1/x
Proof
Trigonometric
sin x = cos x
Proof
csc x = -csc x cot x
Proof
cos x = - sin x
Proof
sec x = sec x tan x
Proof
tan x = sec
2
x
Proof
cot x = - csc
2
x
Proof
Inverse Trigonometric
arcsin x =
1
(1 - x
2
)
arccsc x =
-1
|x|
(x
2
- 1)
arccos x =
-1
(1 - x
2
)
arcsec x =
1
|x|
(x
2
- 1)
arctan x =
1
1 + x
2
arccot x =
-1
1 + x
2
Hyperbolic
sinh x = cosh x
Proof
csch x = - coth x csch x
Proof
cosh x = sinh x
Proof
sech x = - tanh x sech x
Proof
tanh x = 1 - tanh
2
x
Proof
coth x = 1 - coth
2
x
Proof
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