Formulario derivadas

Formulario de derivadas completo, con identidades trigonométricas

1. IIDDEENNTTIIDDAADDEESS TTRRIIGGOONNOOMMEETTRRIICCAASS
A
A
A
senA
AA
AA
AsenA
AA
AA
AAsen
AA
AAsen
AsenAA
AsenAAsen
sec
cos
1
csc
1
1cottan
1seccos
1csc
1
2
cot
2
csc
1
2
tan
2
sec
1
2
cos
2
2cos
2
1
2
12
cos
2cos
2
1
2
12
22
cos2cos
cos22
=
=
=
=
=
=−
=−
=+
+=
−=
−=
=
   
   
   
( ) ( )
( ) ( )
( ) ( )
 
 
A
A
BA
BA
BA
senAsenBBABA
AsenBBsenABAsen
BAsenBAsenBsenA
BABABA
BABAsenAsenB
BABAsensenBsenA
ABsenBAsenBA
BABABA
tan
1
cot
tantan1
tantan
]tan[
coscoscos
coscos
2
1
2
1
cos
cos
2
1
cos
2
1
coscos
cos
2
1
cos
2
1
2
1
cos
2
1
2
2
1
2
1
2coscos
2
1
cos
2
1
cos2coscos
=

=
=
=
++−=
++−=
+−−=
−+=+
−+=−
−+=+

A
A
A
A
A
senA
senA
A
A
A
senA
A
A
A
A
AA
AA
sen
tan
cot
1
sec
1
cos
csc
1
cos
cot
cos
tan
cos1
cos1
tan
2
cos1
2
cos
2
cos1
2
=
=
=
=
=
+
−
=
+
=
−
=

DERIVADAS ()
()
()
2
1
)(
0
v
dx
dv
u
dx
du
v
v
u
dx
d
dx
dun
nu
n
u
dx
d
dx
du
v
dx
dv
uuv
dx
d
dx
du
ccu
dx
d
dx
dw
dx
dv
dx
du
wvu
dx
d
dx
cd
−
=





−
=





+=
=
++=++
=

DERIVADAS
TRIGONOMETRICAS ()
()
()
()
()
()
dx
du
uuu
dx
d
dx
du
uuu
dx
d
dx
du
uu
dx
d
dx
du
uu
dx
d
dx
du
senuu
dx
d
dx
du
usenu
dx
d
cotcsccsc
tansecsec
2
csccot
2
sectan
cos
cos
−=
=
−=
=
−=
=

DERIVADA DE UN
ANGULO ( )
( )
( )
( )
( )
( )
1
2
/
csc
2
1
/
cot
2
1
/
cos
1
2
/
sec
2
1
/
tan
2
1
/
−
−
=
+
−
=
−
−
=
−
=
+
=
−
=
uu
dxdu
uArc
dx
d
u
dxdu
uArc
dx
d
u
dxdu
uArc
dx
d
uu
dxdu
uArc
dx
d
u
dxdu
uArc
dx
d
u
dxdu
Arcsenu
dx
d

DERIVADAS DE FUNCIONES EXPONENCIALES Y LOGARITMICAS dx
du
u
e
au
a
dx
d log
log=





dx
du
a
u
a
u
a
dx
d
ln=




 ()
u
dxdu
u
dx
d /
ln= dx
duu
e
u
e
dx
d
=






DERIVADAS
TRIGONOMETRICAS A LA “N” ()
)'(
2
sec
1
tan'
tan
'
1
cos'
cos
)'(cos
1
'
uuu
n
ny
u
n
y
uusenu
n
ny
u
n
y
uuu
n
nseny
u
n
seny
−
=
=
−
−=
=
−
=
=
)'(
2
csc
1
cot'
cot
)'(cotcsc
1
csc'
csc
)'(tansec
1
sec'
sec
uuu
n
ny
u
n
y
uuuu
n
ny
u
n
y
uuuu
n
ny
u
n
y
−
−=
=
−
−=
=
−
=
=

Propiedades de
Logaritmos ()
1ln
lnln
lnlnln
lnlnln
=
=
−=
+=
e
An
n
A
BA
B
A
BABA
()
()
()
()
()()
()( )
()( )
3322
3322
22
32233
32233
222
222
33
33
2
2
babababa
babababa
bababa
babbaaba
babbaaba
bababa
bababa
+=+−+
−=++−
−=−+
−+−=−
+++=+
+−=−
++=+

Exponentes y Radicales ()
m
n
a
n
m
a
nm
a
n
b
n
a
n
b
n
a
n
b
a
n
b
n
a
n
b
n
a
n
ab
n
a
n
a
x
b
x
a
x
b
a
x
b
x
a
x
ab
xy
a
y
x
a
yx
a
y
a
x
a
yx
a
y
a
x
a
x
a
x
a
a






==
==





==
=
=





=
=





−
=
+
=
=
−
=
1
1
11
1
1
1
0
()
()
()
()
()
() 





csccsc
secsec
cotcot
tantan
coscos
−=−
=−
−=−
−=−
=−
−=− sensen


Fórmula General 0
2
=++ cbxax
a
acbb
x
2
4
2
−−
=



H CO



CA CO
H
CA
H
CO
CA
CA
CO
H
CA
H
CO
sen
=
=
=
=
=
=






csc
sec
cot
tan
cos

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