Transformadas

Derivadas
Reglas de derivaci´n
o

Suma

Producto

d
[f (x) + g (x)] = f (x) + g (x)
dx
d
[kf (x)] = kf (x)
dx
d
[f (x)g (x)] = f(x)g (x) + f (x)g (x)
dx

Cociente

Regla de la cadena

d f (x)
f (x)g (x) − f (x)g (x)
=
dx g (x)
g (x)2
d
{f [g (x)]} = f [g (x)]g (x)dx
d
{f (g [h(x)])} = f (g [h(x)])g [h(x)]h (x)
dx
d
(k ) = 0
dx
dk
(x ) = kxk−1
dx

Potencia

d
[f (x)k ] = kf (x)k−1 f (x)
dxd√
d 1 /2
1
( x) =
(x ) = √
dx
dx
2x

d
[
dx

d
dx

d
1
f (x)
=−
dx f (x)
f (x)2

1
x

=

d −1
1
(x ) = − 2
dx
xf (x)] =

f (x)
2

f (x)

Reglas de derivaci´n (continuaci´n)
o
o
d
(sin x) = cos x
dx

d
[tan f (x)] = [1 + tan2 f (x)]f (x)
dxd
[arcsin f (x)] =
dx

d
−1
(arc cos x) = √
dx
1 − x2

d
[arc cos f (x)] =
dx

d
1
(arctan x) =
dx
1 + x2

d
f (x)
[arctanf (x)] =
dx
1 + f (x)2

dx
(e ) = ex
dx

d f (x)
) = ef (x) f (x)
(e
dx

dx
(a ) = ax ln a
dx

d f (x)
) = af (x) ln af (x)
(adx

d
1
(ln x) =
dx
x

Exponenciales

d
[cos f (x)] = − sin f (x)f (x)
dx

d
1
(arcsin x) = √
dx
1 − x2
Funciones de arco

d(cos x) = − sin x
dx
d
(tan x) = 1 + tan2 x
dx

Trigonom´tricas
e

d
[sin f (x)] = cos f (x)f (x)
dx

d
f (x)
(ln f (x)) =
dx
f(x)

d
11
(lg x) =
dx a
x ln a

d
f (x) 1
(lg f (x)) =
dx a
f (x) ln a

f (x)
1 − f (x)2
−f (x)
1 − f (x)2

Logar´
ıtmicas