Salvador Vera

3.2. FUNCIÓN DERIVADA. REGLAS DE DERIVACIÓN. 161
Derivada de las funciones elementales:
función derivada
k 0
x 1
xr rxr−1 √ 1
x
n√ x
ln x
lg b x
1
x ln b
2 √ x
1
n n√ x n−1
1
x
1
=
x lgb e
e x e x
a x a x ln a
x x x x (ln x +1)
sen x cos x
cos x − sen x
tg x
1
cos2 x =sec2 sec x =
x
1
cos x
sec x tg x
csc x = 1
sen x
− csc x cot x
cot x
−1
sen2 x = − csc2 x
arc sen x
1
√
1 − x2 arc cos x
−1
√
1 − x2 arc tg x
1
1+x2 arc sec x
1
|x| √ x2 arc csc x
− 1
−1
|x| √ x2 − 1
arc cotg x
−1
1+x2 senh x cosh x
cosh x senh x
tgh x
1
cosh 2 x
función derivada
k 0
u u ′
ur rur−1u ′
√ u
u
′
n√ u
ln u
lg b u
u ′
u ln b
2 √ u
u ′
n n√ u n−1
u ′
u
= u′
u lg b e
e u e u u ′
a u a u u ′ ln a
′ f
f
f g f gg ′ ln f + g
sen u u ′ cos u
cos u −u ′ tg u
sen u
sec u = 1
cos u
u ′ csc u =
sec u tg u
1
sen u
−u ′ cot u
csc u cot u
arc sen u
arc cos u
arc tg u
arc sec u
arc csc u
arc cotg u
u ′
cos 2 u = u′ sec 2 u
−u ′
sen 2 u = −u′ csc 2 u
u ′
√
1 − u2 −u ′
√
1 − u2 u ′
1+u2 u ′
|u| √ u2 − 1
−u ′
|u| √ u 2 − 1
−u ′
1+u 2
senh u u ′ cosh u
cosh u u ′ senh u
tgh u
u ′
cosh 2 u