1 P Tabla De Derivadas E Integrales

Análisis I

Tabla-26/C

FISICANET

fisicanet@interlap.com.ar
Tabla de Derivadas e Integrales
Función

Dervada

Integral

y=c

y' = 0

c.x

y = c.xy' = c

c.x2/2

y = xn

y' = n.xn-1

xn+1/n+1

y=xn

y’ = -1/(n.xn-1)

x-n+1/-n+1

y = x½

y’ = 1/(2.x½)

2.x3/2/3

y = xa/b

y' = a.x(a/b)-1/bx(a/b)+1/[(a/b)+1]

y = 1/x

y' = -1/x2

ln x

y = sen x

y' = cos x

-cos x

y = cos x

y' = -sen x

-

sen x

2

y = tg x

y' = 1/cos x

y = cotg x

y' =-1/sen2x

-ln cos x
ln sen x
2

y = sec x

y' = sen x/cos x

ln (tg ½.x)

y = cosec x

y' = -cos x/sen2x

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

2 ½

y = arcsen xy' = 1/(1 - x )

x.arcsen x + (1 - x2)½

y = arccos x

y' = -1/(1 - x2)½

x.arccos x - (1 - x2)½

y = arctg x

y' = 1/(1 + x2)

x.arctg x - ½ln (1 +x2)

y = arccotg x

y' = -1/(1 + x2)

x.arccotg x + ½ln (1 + x2)

y = arcsec x

y' = 1/[x.(x2 -1)½]

1

y = arccosec x

y' = -1/[x.(x2 – 1)½]

2

y =senh x

y' = cosh x

cosh x

y = cosh x

y' = senh x

senh x

2

y = tgh x

y' = sech x

ln cosh x

y = cotgh x

y' = -cosech2x

ln senh x

y = sech xy' = -sech x.tgh x

3

y = cosech x

y' = -cosech x.cotgh x

4

y = ln x

y' = 1/x

x.(ln x - 1)

y = logax

y' = 1/x.ln a

x.( logax - 1/ln a)

y=ex

y' = e

x

ex

y = ax

y' = ax.ln a

ax/ln a

y = xx

y' = xx.(ln x + 1)

5

y = eu

y’ = eu.u’

6

y = u.v

y' = u'.v + v'.u

y = u/v
y=u

v

y =lnuv

y' = (u'.v - v'.u)/v

∫u.dv + ∫v.du
2

7

v

y' = u .(v'.lnu + v.u'/u)

8
2

y’ = (v’.u.lnu - u’.v.lnv)/v.u.ln u

9

Ricardo Santiago Netto