Tabla De Derivabas e Integrales

y=c y = cx

Función 0

Tabla de derivadas e integrales Derivada

y = cx
c x2 2

Integrada

y' = c
y ' = nx n −1

y = xn y = x −n

y' = −
1 2

y= x=x

y' =
b

1 nx n −1 1
1 22x
bx

x n +1 n +1 x − n +1 − n +1 2 32 x 3
x b a +1 b ln x

y = b xa = x

a

y' =

(a b −1)

a

(a +1)

y=

1 x

y' = −

1 x2

y=sen x y=cos x y=tg x y=cotg x y=sec xy’=cos x y’=-sen x

y' =

1 = sec 2 x 2 cos x 1 y' = = sec 2 x 2 sen x senx y ' = sec xtgx = cos 2 x
y ' = − cos ecx cot gx = − y' = 1 1− x2 1 cos x sen 2 x

-cos x sen x -ln cos x ln sen xln tg

x = ln sec x + tgx 2

y=cosec x y=arcsen x

ln(cosec x-cotg x)

x.arcsenx + 1 − x 2 x. arccos x − 1 − x 2
x.arctgx − x.arctgx + ln 1 + x 2 2 ln 1 + x 2
x2 −1   x2  

y=arccos xy' = −

y=arctg x

1− x2 1 y' = 1+ x2

y=arccotg x

1 y' = − 1+ x2 y' = 1 x x −1
2

Y=arcsec x

2  xArcSecx − ln x1 +  

Y=arccosec x

y' = −

1 x x2 − 1
cosh x

y=senh xy’=cosh x

y=cosh x y=tgh x y=cotgh x y=ln x

y’=senh x

y '= sec h x y ' = − cos ech 2 x 1 y '= x 1 y '= x ln a y' = e x

2

senh x ln cosh x ln senh x

x ln x − x

y = log a x y =ex

− x + x ln x ln a

ex y '= ax ln a

y = ax y = eu y = uv

y '= a x ln a y' = e u u' y ' = u ' v + uv'

u v y = uv y= y = ln u v

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' =
Formula de recurrencia

∫ udv + ∫ vdu

∫ (x

dx
2

+ 1)

2

=

2(x + 1)
2

x

+

1 arctgx 2
b

Propiedades Integrales definidassi k=cte

∫ kf
a

b

x

dx = k ∫ f x dx
a
b c b

Aditiva: si

c ∈ (a, b ) ⇒ ∫ f x dx = ∫ f x dx + ∫ f x dx
a a c

∫f
a

a

x

dx = 0
a

∫
a

b

f x dx = − ∫ f x dx
bRegla de Barrow

∫f
a

b

x

dx = F(b ) − F(a ) 1 f ( x ) dx b−a∫ a
b

Teorema del valor medio del calculo integral

f (c ) =

Identidades Trigonometricas

sen 2 x + cos 2 x = 1...