matematicas

Derivadas
Reglas de derivación

Suma
Resta
Producto de una función y un número
Cociente de una función y un número
Producto
Cociente
Composición (regla de la cadena)
Función inversa

[f(x) + g(x)]0 = f 0 (x) + g 0 (x)
[f (x) − g(x)]0 = f 0 (x) − g 0 (x)
[k · f (x)]0 = k · f 0 (x)
0

(x)
[ f (x) ]0 = f k
k
[f (x) · g(x)]0 = f 0 (x) · g(x) + f (x) · g 0 (x)
∙
¸0
f 0 (x) ·g(x) − f (x) · g 0 (x)
f (x)
=
g(x)
g(x)2
0
0
(g ◦ f ) (x) = (g[f (x)]) = g 0 [f (x)] · f 0 (x)
1
(f −1 )0 [f (x)] = 0
f (x)

f y g funciones
f y g funciones
f y g funciones, k número
f yg funciones, k número
f y g funciones
f y g funciones
f y g funciones
f y g funciones

Derivadas de funciones usuales

Constante
Potencia
Exponencial
Exponencial de base e
LogaritmoLogaritmo de base e
Seno
Coseno
Tangente
Cotangente
Arcoseno
Arcocoseno
Arcotangente
Seno hiperbólico
Coseno hiperbólico
Argumento seno hiperbólico
Argumento coseno hiperbólico

(k)0 = 0
(xn)0 = nxn−1
(ax )0 = ax · log a
(ex )0 = ex
1
1
(loga x)0 = x ·
log a
(log x)0 =

1
x

(sin x)0 = cos x
(cos x)0 = − sin x
1
(tan x)0 =
cos2 x
1
(cot x)0 = − 2
sin x
1
0
(arcsinx) = √
1 − x2
1
(arccos x)0 = − √
1 − x2
1
(arctan x)0 =
1 + x2
0
(sinh x) = cosh x
(cosh x)0 = sinh x
1
(arg sinh x)0 = √
1 + x2
1
(arg cosh x)0 = √
2−1
x

1

[f (x)n ]0 = nf(x)n−1 f 0 (x)
[af (x) ]0 = af (x) · f 0 (x) · log a
(ef (x) )0 = ef (x) · f 0 (x)
f 0 (x)
1
(loga [f (x)])0 =
·
f (x) log a
f 0 (x)
(log[f (x)])0 =
f (x)
(sin[f (x)])0 = cos[f (x)] · f 0 (x)(cos[f (x)])0 = − sin[f (x)] · f 0 (x)
f 0 (x)
(tan[f (x)])0 =
cos2 [f (x)]
f 0 (x)
(cot[f (x)])0 = − 2
sin [f (x)]
f 0 (x)
0
(arcsin[f (x)]) = p
1 − f (x)2
f 0 (x)
(arccos[f (x)])0 = − p1 − f (x)2
f 0 (x)
(arctan[f (x)])0 =
1 + f (x)2
0
(sinh[f (x)]) = cosh[f (x)] · f 0 (x)
(cosh[f (x)]0 = sinh[f (x)] · f 0 (x)
f 0 (x)
(arg sinh[f (x)])0 = p
1 + f (x)2
f 0 (x)
(arg...