Cálculo Diferencial e Integral I

3.7 TABELA GERAL DE DERIVADA
Na tabela que se segue u, v são funções deriváveis de x e c ,α , a são
constantes reais.
(1)
(2)
(3)
(4)
(5)
y = c ⇒ y′
= 0
y = x ⇒ y′
= 1
y = c ⋅ u ⇒ y′
= c ⋅u′
y = u + v ⇒ y′
= u′
+ v′
y = u ⋅ v ⇒ y′
= u′
⋅ v + u ⋅ v′
(6)
y =
u
v
⇒
y′
=
u′
⋅ v − u ⋅
2
v
v′
(7)
y = u
α
⇒
y′
=
−1
α u
α
⋅ u′
, ( α ≠ 0)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
u
u
y = a ⇒ y′
= a ⋅ ln a ⋅ u′
, ( a > 0,
a ≠ 1)
u u
′
y = e ⇒ y′
= e
⋅ u
1
y = loga
u ⇒ y′
= ⋅ u′
, ( a > 0,
a ≠ 1)
u ⋅ ln a
1
y = lnu
⇒ y′
= ⋅ u′
u
y = senu
⇔ y′=
(cosu)
⋅ u′
y = cosu
⇔ y′
= ( − sen u)
⋅ u′
y = tg u ⇔ y′
= (sec u)
⋅ u′
y = secu
⇔ y′
= (se c u ⋅ tg u)
⋅ u′
y = cotg u ⇔ y′
= ( − cossec u)
⋅ u′
y = cossec u ⇔ y′=
( −cossecu⋅
cotgu)
⋅ u′
1
y = arcsenu
⇔ y′
= ⋅ u′
2
1−
u
− 1
y = arccosu
⇔ y′
= ⋅ u′
2
1−
u
1
y = arctgu
⇔ y′
= ⋅ u′
2
1 + u
2
2
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