Formulario de derivadas

FORMULARIO DE DERIVADAS
Siendo a, c constantes y F, G funciones de X derivables en un intervalo I
X son:
1.
Algebraicas:

2.

a

(c )′ = 0

c

(X )′ = c.X

e
g

cc
e

d

(a.X )′ = a.c.X

(c.F )′ = c.F ′

f

(F ± G )′ = F ′ ± G ′

(F .G )′ = F .G ′ + G.F ′

h

′
G.F ′ − F .G ′
F 
;G ≠ 0
  =
G2
G 

c

n −1

c

c −1

′(F )
c

= c.F

(e )′ = e
(c )′ = c
X

X

F

F

c −1

.F ′

b
d

.Ln(c ).F ′

f

1
X
′
(Ln(F ))′ = F
F

(Ln( X ))′ =

(Log (F ))′ =

b
d

F′
F .Ln(10 )

f

′
1 
c1 
1  − 1
 F  = .F  c  .F ′


c


(e F )′ = e F .F ′
(F G )′ = G.F G −1.F ′ + F G .Ln(F ).G ′
1
X .Ln(c )
′
(Logc (F ))′ = F
F .Ln (c )
′
′
(LogG (F ))′= G.Ln(G ).F − F2 .Ln(F ).G
F .G.Ln (G )

(Logc ( X ))′ =

Trigonométricas:
a
c
e
g
i

5.

( X )′ = 1

e
Logarítmicas:
a

4.

b

Potencial y exponencial:
a

3.

⇒las derivadas con respecto a

(Sen( X ))′ = Cos ( X )
(Tan( X ))′ = Sec 2 ( X )
(Sec ( X ))′ = Sec ( X ).Tan( X )
(Sen(F ))′ = Cos (F ).F ′
(Tan(F ))′ = Sec 2 (F).F ′
(Sec (F ))′ = Sec (F ).Tan(F ).F ′

k
Trigonométricas inversas
a
c
e
g
i
k

(ArcSen ( X ))′ =

1
2

1− X
(ArcTan ( X ))′ = 1 2
1+ X
1
(ArcSec ( X ))′ =
X. X 2−1
′
(ArcSen (F ))′ = F 2
1− F
′
(ArcTan(F ))′ = F 2
1+ F
F′
(ArcSec (F ))′ =
F. F 2 − 1

l

(Cos ( X ))′ = −Sen( X )
(Cot ( X ))′ = −Csc 2 ( X )
(Csc ( X ))′ = −Csc (X ).Cot ( X )
(Cos (F ))′ = −Sen(F ).F ′
(Cot (F ))′ = −Csc 2 (F ).F ′
(Csc (F ))′ = −Csc (F ).Cot (F ).F ′

b

(ArcCos ( X ))′ = −

b
d
f
h
j

d
f
h
j
l

1

1− X2
(ArcCot ( X ))′ = − 1 2
1+ X
1
(ArcCsc ( X ))′ = −
X. X 2 −1
′
(ArcCos (F ))′ = − F 2
1− F
′
(ArcCot (F ))′ = − F 2
1+ F
′
(ArcCsc (F ))′ = − F 2
F. F − 1