Standard Derivatives and Integrals Flashcards
Derivative of
xn
nxn-1
Derivative of
ex
ex
Derivative of
ln x
1 / x
Derivative of
sin x
cos x
Derivative of
cos x
- sin x
Derivative of
tan x
sec2 x = 1 / cos2 x
Derivative of
ln(cos x)
- tan x
Derivative of
sin−1 x
1 / √(1−x2)
Derivative of
cos-1 x
- 1 / √ ( 1 - x2)
Derivative of
tan−1 x
1 / (1 + x2)
Derivative of
sinh x
cosh x
Derivative of
cosh x
sinh x
Derivative of
tanh x
sech2 x = 1 / (cosh2 x)
Derivative of
sinh-1 x
1 / √(1 + x2)
Derivative of
cosh-1 x
1 / √( −1 + x2)
Derivative of
tanh−1 x
1 / (1−x2)
Derivative of
(ax + b)n
a n (ax + b)<em>n</em> - 1
Derivative of
e(<em>ax</em> + <em>b</em>)
a e(<em>ax</em> + <em>b</em>)
Derivative of
ln (ax + b)
a / (ax + b)
Derivative of
sin (ax + b)
a cos (ax + b)
Derivative of
cos (ax + b)
-a sin (ax + b)
Derivative of
tan (ax + b)
a sec2 (ax + b) = a / cos2 (ax + b)
Derivative of
ln (cos (ax + b))
-a tan(ax + b)
Derivative of
sin−1 (ax + b)
a / √(1 − (ax + b)2)
Derivative of
cos-1 (ax + b)
- a / √ (1 − (ax + b) 2)
Derivative of
tan−1 (ax + b)
a / (1 + (ax + b)2)
Derivative of
sinh (ax + b)
a cosh (ax + b)
Derivative of
cosh (ax + b)
a sinh (ax + b)
Derivative of
tanh (ax + b)
a sech2 (ax + b) = a / (cos2 (ax + b))
Derivative of
sinh-1 (ax + b)
a / √(1 + (ax + b)2)
Derivative of
cosh-1 (ax + b)
a / √( -1 + (ax + b)2)
Derivative of
tanh−1 (ax + b)
a / (1 − (ax + b)2)
Here, a, b, n are … and x is the independent variable
constants
Here, a, b, n are constants and x is … .
the independent variable
