Tabla de derivadas y equivalentes

Función
Derivada
Función
Derivada
k
0
senu
cosu ⋅ u ′
x
1
cosu
-senu ⋅ u ′
tgu
1
u ′ = 1 + tg 2 u ⋅ u ′
2
cos u
un
1
u
u
n
u
nun-1 u ′
−
u′
u2
u′
2 u
u′
n n u n −1
(
1
⋅ u′
1 +u 2
1
⋅ u′
2
1− u
1
−
⋅ u′
2
1− u
Arctgu
Arcsenu
Arccosu
u
u ′ ⋅ sgu
shu
chu ⋅ u ′
ex
ex
chu
shu ⋅ u ′
eu
e u ⋅ u′
thu
ax
a x ln a
Arshu
au
a u ln a ⋅ u ′
Archu
lnu
1
u′
u
Arthu
log a x
1
x ln a
uv
)
1
u′
ch 2 u
1
⋅ u′
1+ u2
1
⋅ u′
u 2 −1
1
⋅ u′
1− u2
u′ 

u v ′ ln u + v ⋅ 
u

v
f ( x)
f ′( x )
k ⋅u
k ⋅ u′
u ±v
u′ ± v ′
u ⋅v
u′ ⋅v + u ⋅v ′
u ′v − uv ′
v2
u
v
Infinitésimos equivalentes
Funciones elementales
x →0
(1 + x )m
m
− 1 ∼mx
1 + x − 1∼
x
m
L (1 + x ) ∼ x
ex − 1∼ x
a x − 1∼ xLa
senx∼x
tgx∼x
1-cosx∼
(1 + x )x
1 2
x
2
− 1∼ x 2
x x − 1 ∼ xLx