Tabla de derivadas

Tabla de Derivadas e Integrales

Función

Derivada

Integral

y=c

y’ = 0

c.x

y = c.x

y’ = c

c.x /2

2

y=x

n

y’ = n.x

n-1

y=x

-n

y’ =-1/(n.x )

y=x

½

y’ = 1/(2.x )

y=x

a/b

y’ = a.x

x
n-1

n+1

x-

½

/n+1

n+1

/-n+1

3/2

2.x /3

(a/b)-1

/b

x

2

(a/b)+1/[(a/b)+1]

y = 1/x

y’ = -1/x

y = sen x

y’ = cos x

-cos x

y = cos x

y’ = -sen x

sen x

y = tg x

y’ = 1/cos x

y = cotg x

y’ = -1/sen x

y = sec x

y’ =sen x/cos x

y = cosec x

y’ = -cos x/sen x

y = arcsen x

y’ = 1/(1 – x )

y = arccos x

y’ = -1/(1 – x )

y = arctg x

y’ = 1/(1 + x )

y = arccotg x

y’ = -1/(1+ x )

y = arcsec x

y’ = 1/[x.(x -1) ]

y = arccosec x

y’ = -1/[x.(x – 1) ]

2

y = senh x

y’ = cosh x

cosh x

y = cosh x

y’ = senh x

senh x

y = tgh xy’ = sech x

y = cotgh x

y’ = -cosech x

ln senh x

y = sech x

y’ = -sech x.tgh x

3

y = cosech x

y’ = -cosech x.cotgh x

4

y = ln x

y’ = 1/x

x.(lnx – 1)

ln x

2

-ln cos x

2

ln sen x
2

ln (tg ½.x)

2

ln [cos x/(1 - sen x)]

2 ½

2 ½

x.arcsen x + (1 – x )

2 ½

2 ½

x.arccos x – (1 – x )

22

x.arctg x – ½ln (1 + x )

2

2

2

x.arccotg x + ½ln (1 + x )
½

2

1
½

2

ln cosh x
2

y = logax

y’ = 1/x.ln a

y=e

x

y’ = e

y=a

xy’ = a .ln a

x

y’ = x .(ln x + 1)

u

x.( logax – 1/ln a)

x

e

x

a /ln a

x

5

y’ = e .u’

u

6

y = u.v

y’ = u’.v + v’.u

u.dv + v.du

y= u/v

y’ = (u’.v – v’.u)/v

y=x

y=e

v

x

x

2

7

v

y=u

y’ = u .(v’.lnu + v.u’/u)

y = lnuv

y’ = (v’.u.lnu – u’.v.lnv)/v.u.ln u

8
2

9