DERIVATIVE RULES
( )
d
( sin x ) = cos x
dx
d
( cos x ) = − sin x
dx
d x
a = ln a ⋅ a x
dx
( )
d
( tan x ) = sec2 x
dx
d
( cot x ) = − csc2 x
dx
d
( f ( x) ⋅ g ( x) ) = f ( x) ⋅ g ′( x) + g ( x) ⋅ f ′( x)
dx
d
( sec x ) = sec x tan x
dx
d ⎛ f ( x) ⎞ g ( x) ⋅ f ′( x) − f ( x) ⋅ g ′( x)
⎜
⎟=
2
dx ⎝ g ( x) ⎠
( g ( x) )
d
1
( arcsin x ) =
dx
1 − x2
d
( f ( g ( x)) ) = f ′( g ( x)) ⋅ g ′( x)
dx
d
1
( arc sec x ) =
dx
x x2 − 1
d
1
( ln x ) =
dx
x
d
( sinh x ) = cosh x
dx
d n
x = nx n −1
dx
d
( csc x ) = − csc x cot x
dx
d
1
( arctan x ) =
dx
1 + x2
d
( cosh x ) = sinh x
dx
INTEGRAL RULES
1
∫ x dx = n + 1 x
n
1
∫ a dx = ln a a
x
n +1
x
+ c , n ≠ −1
+c
1
∫ x dx = ln x + c
∫
dx
1 − x2
dx
∫ 1+ x
∫x
2
= arcsin x + c
= arctan x + c
dx
x2 −1
= arcsec x + c
∫ sin xdx = − cos x + c
∫ csc
∫ cos xdx = sin x + c
∫ sec x tan xdx = sec x + c
∫ sec
∫ csc x cot xdx = − csc x + c
2
xdx = tan x + c
∫ sinh xdx = cosh x + c
2
xdx = − cot x + c
∫ cosh xdx = sinh x + c