1.
a
=
y
0y
=
′
2.
n
xay ⋅=
1-n
xany ⋅⋅=
′
3.
n
fy )(=
ffny
n
′
⋅⋅=
′
−1
)(
4.
L(x)y
=
x
1
y=
′
5.
(
)
fLy =
f
f
y
′
=
′
6.
)(log
xy
a
=
)(log
1e
x
y
a
⋅=
′
7.
(
)
fy
a
log=
)(log e
f
f
y
a
⋅
′
=
′
8.
x
ay =
)(aLay
x
⋅=
′
9.
f
ay =
)(aLafy
f
⋅⋅
′
=
′
10.
x
ey =
x
e=
′
y
11.
f
ey =
f
efy ⋅
′
=
′
12.
n
fy =
nn
fn
f
y
1
)(
−
⋅
′
=
′
13.
gfy
⋅
=
fggfy
⋅
′
+
⋅
′
=
′
14.
g
f
y=
2
g
fggf
y
⋅
′
−
⋅
′
=
′
15.
senx
y
=
xy cos
=
′
16.
(
)
fseny =
(
)
ffy cos⋅
′
=
′
17.
(
)
fseny
n
=
(
)
(
)
fcosffsenny
1n
⋅
′
⋅⋅=
′
−
18.
cosx
y
=
senxy
−
=
′
19.
(
)
fy cos=
(
)
fsenf-y ⋅
′
=
′
20.
(
)
f
n
cosy =
(
)
(
f
senffny
n
⋅
′
⋅⋅−=
′
−1
cos
21.
tgx
y
=
xtg
x
y
2
2
1
cos
1+==
′
22.
(
)
ftgy =
( ) (
[
f
tgf
f
f
y
2
2
1
cos +⋅
′
=
′
=
′
23.
(
)
f
n
tgy =
( ) ( )
f
ftgny
n
2
1
cos
f
′
⋅⋅=
′
−
24.
gx
y
cot
=
(
)
xg
x
sen
y
2
2
cot1
1+−=
−
=
′
25.
(
)
fgy cot=
( )
fsen
f
y
2
′
−
=
′
26.
(
)
fgy
n
cot=
( ) ( )
fsen
f
fgny
n
2
1
cot
′
⋅⋅−=
′
−
27.
x
y
sec
=
tgxxy
⋅
=
′
sec
28.
(
)
fy sec=
(
)
(
)
ftgffy ⋅⋅
′
=
′
sec
29.
ecx
y
cos
=
gxecxy cotcos
⋅
−
=
′
30.
(
)
fecy cos
=
(
)
(
)
fgfecfy cotcos ⋅⋅
′
−=
′
31.
arcsenx
y
=
2
1
1
x
y−
=
′
32.
(
)
farcseny =
( )
2
f1
f
y−
′
=
′
33.
x
y
arccos
=
2
1
1
x
y−
−
=
′
34.
(
)
fy arccos=
( )
2
1f
f
y−
′
−
=
′
35.
arctgx
y
=
2
1
1
x
y+
=
′
36.
(
)
farctgy =
( )
2
1
f
f
y+
′
=
′
37.
gx
arc
y
cot
=
2
1
1
x
y+
−
=
′
38.
(
)
fgarcy cot
=
( )
2
1
f
f
y+
′
−
=
′
39.
x
arc
y
sec
=
1
1
2
−⋅
=
′xx
y
40.
(
)
farcy sec=
( )
1
2
−⋅
′
=
′ff
f
y
41.
ecx
y
arccos
=
1
1
2
−⋅
−
=
′xx
y
42.
(
)
fecy arccos
=
( )
1
2
−⋅
′
−
=
′ff
f
y
43. Derivación logarítmica:-
(
((
(
)
))
)
fy
g
=
==
=
1º) Tomar L (logaritmos neperianos) en ambos
miembros:
.LfgLy ⋅
⋅⋅
⋅=
==
=
2º) Derivar en ambos miembros:
.
f
f
gLfg
y
y′
′′
′
⋅
⋅⋅
⋅+
++
+⋅
⋅⋅
⋅
′
′′
′
=
==
=
′
′′
′
3º) Despejar
y
′
′′
′
de la expresión anterior:
(
((
( )
))
)
.f
f
f
gLfgy
g
⋅
⋅⋅
⋅
′
′′
′
⋅
⋅⋅
⋅+
++
+⋅
⋅⋅
⋅
′
′′
′
=
==
=
′
′′
′
FORMULARIO DE DERIVADAS
Mg. López Michelini