FÓRMULAS_BÁSICAS_DERIVADA_E_INTEGRAIS.pdf

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FÓRMULAS BÁSICAS DE DERIVADAS E INTEGRAIS 
[Digite o nome da empresa] 
 
 
Função Derivada 
( ) ,f u k k= ∈ℜ ´( ) 0f u = 
( ) ,nf u u n= ∈ℜ 1(´ ) . nf u n u −= 
( ) . ( )f u k f u= (´ ) . 'f u k f (u)= 
( )f u u= '( ) 1f u = 
vuxf .)( = '( ) . ' '.f x u v u v= + 
v
u
xf =)( ' '. . '( )
²
u v u vf x
v
−
= 
( ) logaf u u= 1
'( )
ln
f x
u a
= 
( ) ,0 1uf u a a= < ≠ '( ) .lnuf u a a= 
( ) lnf u u= 1
'( )f u
u
=
 
( )f u sen u= '( ) cosf u u= 
( ) cosf u u= '( )f u sen u= − 
( )f u tg u= 2'( ) secf u u= 
( )f u sec u= '( )f u sec u .tg u= 
( )f u cossec u= '( )f u -cotg u.cossec u= 
( )f u cotg u= '( ) 2f u cossec u= − 
( ) uf u e= '( ) uf u e= 
( )f u arc cosu= 
2
1
'( )
1
f u
u
= −
−
 
( )f u arc senu= 
2
1
'( )
1
f u
u
=
−
 
( )f u arc tg u= 
2
1
'( )
1
f u
u
=
+
 
Integral Primitiva 
du =∫ u c+ 
k du =∫ .k u c+ 
nu du =∫ 
1
1
n
u
c
n
+
+
+
 
du
u
=∫ 
ln u c+ 
senu du =∫ cosu c− + 
cosu du =∫ senu c+ 
2sec u du∫ tg u c+ 
2cosec u du =∫ cotg u + c− 
secu.tg u du =∫ secu+c 
ue du =∫ 
ue c+ 
ua du =∫ ( 0, 1)
ln
u
a
c a a
a
+ > ≠
 
2
1
1 u
=
−
∫ 
arc sen u + c 
2
1
1 x
=
+
∫ 
arc cos u + c 
2
1
1 x
=
+∫
 
arc tg u c+ 
sen ax dx =∫ 1 cos ax c
a
− + 
cos ax dx =∫ 1 sen ax c
a
+