cy = cx y = cx y = cy =` 2 x c xy = ` = n nx y 1 + n xn = 1 ` − = nx y 1 +

Tabla de derivadas e integrales
Derivada
Función
y=c
y = cx
0
y' = c
c
y = xn
y ' = nx n −1
y = x −n
y' = −
y= x=x
1
y' =
2
y = b xa = x
a
b
1
x
y=sen x
y=cos x
y=tg x
y=cotg x
y=sec x
y=cosec x
y=arcsen x
y=arccos x
y=arctg x
y=arccotg x
Y=arcsec x
Y=arccosec x
y=senh x
1
2x
2
y' = −
x b
a
+1
b
ln x
(a b −1)
1
x2
y’=cos x
y’=-sen x
-cos x
sen x
-ln cos x
1
= sec 2 x
2
cos x
1
y' =
= sec 2 x
2
sen x
senx
y ' = sec xtgx =
cos 2 x
y' =
y ' = − cos ecx cot gx = −
y' =
y' = −
x2
2
(a +1)
a
y' =
ln sen x
ln tg
cos x
sen 2 x
x
= ln sec x + tgx
2
ln(cosec x-cotg x)
1
x.arcsenx + 1 − x 2
1− x2
1
x. arccos x − 1 − x 2
1− x2
1
y' =
1+ x2
x.arctgx −
1
y' = −
1+ x2
x.arctgx +
y' =
1
x x −1
y' = −
Integrada
x n +1
n +1
x − n +1
− n +1
2 32
x
3
1
nx n −1
1
bx
y=
y = cx
2
2
ln 1 + x 2
2

xArcSecx − ln x1 +


1
x x2 − 1
y’=cosh x
ln 1 + x 2
cosh x
x 2 − 1 
x 2 
y=cosh x
y=tgh x
y=cotgh x
y’=senh x
senh x
ln cosh x
2
y '= sec h x
y ' = − cos ech 2 x
1
y '=
x
1
y '=
x ln a
ln senh x
y = ex
y' = e x
ex
y = ax
y '= a x ln a
y = eu
y = uv
y' = e u u'
y ' = u ' v + uv'
u
v
y = uv
u ' v − uv'
v2
vu ' 

y ' = u v  v' ln u +

u 

(v' u ln u − u ' v ln v )
y' =
vu ln 2 u
y=ln x
y = log a x
y=
y = ln u v
x ln x − x
− x + x ln x
ln a
y '=
ax
ln a
∫ udv + ∫ vdu
y' =
Formula de recurrencia
∫ (x
dx
2
=
+ 1)
2
x
2(x + 1)
2
+
1
arctgx
2
Propiedades Integrales definidas
b
∫ kf
si k=cte
b
x
a
Aditiva: si
dx = k ∫ f x dx
a
b
c
b
a
a
c
c ∈ (a, b ) ⇒ ∫ f x dx = ∫ f x dx + ∫ f x dx
a
∫f
x
dx = 0
a
b
a
f x dx = − ∫ f x dx
∫
a
b
Regla de Barrow
b
∫f
x
dx = F(b ) − F(a )
a
Teorema del valor medio del calculo integral
b
f (c ) =
1
f ( x ) dx
b − a ∫a
Identidades Trigonometricas
sen 2 x + cos 2 x = 1
1
cos x
1 + cot g 2x = cos ec 2 x
sec x =
tgx =
senx
cos x
1
senx
sen(x ± y ) = senx. cos y ± seny. cos x
cos ecx =
tgx ± tgy
1 ± tgx.tgy
sen(2 x ) = 2 senx. cos x
1 − cos x
 x
sen  = ±
2
 2
1 + cos x
 x
cos  = ±
2
 2
tg (x ± y ) =
1 − cos 2 x
2
cos( x ± y ) = cos x. cos y ± seny.senx
cos(2 x ) = cos 2 x − sen 2 x
cos(2 x) = 1 − 2 sen 2 x = 2 cos 2 x − 1
1 + cos 2 x
2
 x+ y  x− y
senx + seny = 2sen
 cos

 2   2 
 x+ y  x− y
cos x + cos y = 2 cos
 cos

 2   2 
sen 2 x =
cos x
senx
2
1 + tg x = sec 2 x
cot gx =
1 − cos x
senx
 x
=
=
tg   = ±
1 + cos x 1 − cox
 2
1 − cos x
=
= cos ecx − cot gx
senx
cos 2 x =
 x− y  x+ y
senx − seny = 2sen
 cos

 2   2 
 x+ y  x− y
cos x − cos y = 2sen
 sen

 2   2 