Tabela de derivadas

Vista previa del material en texto

Tabela de derivadas 
 
 
Nesta tabela, u e v são funções deriváveis na variável x. São constantes reais c, n e a. 
 
( )
( )
( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
1
1
2
1 ' 0
2 '
3 ' '
4 ' ln ' , 0 e 1
'5 log , 0 ' , 0 e 1
ln
'6 ln , 0 '
7 sen ' cos '
8 cos ' sen '
9 tg ' sec '
10 cotg
n n
n n
u u
u
a
 y c y
 y x y n x
 y u y n u u
 y a y a a u a a
u y u y a a
u a
u y u u y
u
 y u y u u
 y u y u u
 y u y u u
y u
−
−
= ⇒ =
= ⇒ = ⋅
= ⇒ = ⋅ ⋅
= ⇒ = ⋅ ⋅ > ≠
= > ⇒ = > ≠⋅
= > ⇒ =
= ⇒ = ⋅
= ⇒ = − ⋅
= ⇒ = ⋅
= ⇒ ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
2
2
2
2
2
2
' cossec . '
11 sec ' sec tg '
12 cossec ' cossec cotg '
'13 arcsen '
1
'14 arccos '
1
'15 arctg '
1
'16 arccotg '
1
'17 arcsec , 1 '
1
18 arccos
y u u
y u y u u u
y u y u u u
uy u y
u
uy u y
u
uy u y
u
uy u y
u
uy u u y
u u
y
= −
= ⇒ = ⋅ ⋅
= ⇒ = − ⋅ ⋅
= ⇒ = −
−= ⇒ = −
= ⇒ = +
−= ⇒ = +
= > ⇒ = −
= ( )
2
'sec , 1 '
1
uu u y
u u
−> ⇒ = −