Tabla_derivadas

Tabla de derivadas
Reglas generales de derivación

1

Regla de la suma-resta

f (x) = u(x) ± v(x)

f (x) = u (x) ± v (x)

Regla del producto1

f (x) = u(x) · v(x)

f (x) = u (x) · v(x) + u(x) · v(x)

Regla del cociente

f (x) =

Regla de la cadena

f (x) = (u ◦ v)(x) = u(v(x))

f (x) = u (v(x)) · v (x)

Inversa de una función

f (x) = u−1 (x)

f (x) =

u(x)
v(x)

f (x) =

u (x)·v(x)−u(x)·v (x)v(x)2

1
(u ◦ u−1 )(x)

=

1
u (u−1 (x))

En general, si f (x) = u1 (x) · u2 (x) · . . . · un (x) entonces
f (x) = u1 (x) · u2 (x) · . . . · un (x) + u1 (x) · u2 (x) · . . . · un (x) + · · · + u1 (x) ·u2 (x) · . . . · un (x).

Tipo

f (x)

f (x)

Constante

f (x) = k

f (x) = 0

Identidad

f (x) = x

f (x) = 1

Potencial

f (x) = xn

f (x) = n xn−1

Irracional

f (x) =

Exponencial

f (x) = ex

f(x) = ex

Exponencial en base a

f (x) = ax

f (x) = ax · log a

Exponencial de funciones

f (x) = g(x)h(x)

f (x) = g(x)h(x) · h (x) · log g(x) +

Logarítmica

f (x) = log x

f (x) =

1
xLogarítmica en base a

f (x) = loga x

f (x) =

1
x·log a

Seno

f (x) = sin x

f (x) = cos x

Coseno

f (x) = cos x

f (x) = − sin x

√
n

x

f (x) =

..
.
1

Restricciones

n

1
√
n n−1
x

con a > 0
h(x)
g(x)· g (x)

con a > 0, a = 1

Tipo

f (x)

f (x)

Tangente

f (x) = tan x

f (x) = 1 + tan2 x =

Cosecante

f (x) = csc x =

1
sin x

f (x) = − csc x · cot x

Secante

f (x) = sec x =

1
cos x

f (x) =sec x · tan x

Cotangente

f (x) = cot x =

1
tan x

f (x) = − csc2 x =

Arco seno

f (x) = arc sin x

f (x) =

√ 1
1−x2

Arco coseno

f (x) = arc cos x

f (x) =

√ −1
1−x2

Arco tangente

f (x) =arc tan x

f (x) =

1
1+x2

Arco cosecante

f (x) = arc csc x

f (x) =

√−1
x x2 −1

Arco secante

f (x) = arc sec x

f (x) =

√1
x x2 −1

Arco cotangente

f (x) = arc cot x

f (x) =

−1
1+x2

Senohiperbólico

f (x) = sinh x

f (x) = cosh x

Coseno hiperbólico

f (x) = cosh x

f (x) = sinh x

Tangente hiperbólico

f (x) = tanh x

f (x) =

Cosecante hiperbólico

f (x) = csch x =

1
sinh x

f (x)...