5.4. Función derivada. Cálculo de derivadas
186
DERIVADAS DE FUNCIONES ELEMENTALES
Función
Derivada
Función
Derivada
C
0
f (x) + g(x)
f ′ (x) + g′ (x)
x
1
c · f (x)
c · f ′ (x)
1
x
−1
x2
1
f (x)
− f ′ (x)
f (x)2
√
x
1
√
2 x
xn
nxn−1
( f (x))n
n( f (x))n−1 · f ′ (x)
ex
ex
e f (x)
e f (x) · f ′ (x)
ax
ax · ln a
a f (x)
ln a · a f (x) · f ′ (x)
ln x
1
x
ln f (x)
f ′ (x)
f (x)
sen x
cos x
sen( f (x))
cos( f (x)) · f ′ (x)
cos x
− sen x
cos( f (x))
− sen( f (x)) · f ′ (x)
tg x
1
cos2 x
tg( f (x))
f ′ (x)
cos2 ( f (x))
arc sen x
√ 1
1−x2
arc sen( f (x))
√f
arc cos x
√−1
1−x2
arc cos( f (x))
√− f
arc tg x
1
1+x2
arc tg( f (x))
f ′ (x)
1+ f (x)2
f (x) · g(x)
f ′ (x) · g(x) + f (x) · g′ (x)
i
h
′ (x)
f (x)g(x)
g′ (x) ln f (x) + g(x) ff (x)
f (x)
g(x)
f ′ (x)·g(x)− f (x)·g′ (x)
(g(x))2
f (x)g(x)
p
f (x)
′
2
f (x)
√
f (x)
′ (x)
1− f (x)2
′ (x)
1− f (x)2
0
