tabla de derivadas e integrales

2Función
Derivada
Integral
y = c
y’ = 0
c.x
y = c.x
y’ = c
c.x2/2
y = xn
y’ = n.xn-1
xn+1/n+1
y = x-n
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/b
x(a/b)+1/[(a/b)+1]
y = 1/x
y’ = -1/x2
ln x
y = sen x
y’ = cosx
-cos x
y = cos x
y’ = -sen x
sen x
y = tg x
y’ = 1/cos2x
-ln cos x
y = cotg x
y’ = -1/sen2x
ln sen x
y = sec x
y’ = senx/cos2x
ln (tg ½.x)
y = cosec x
y’ = -cos x/sen2x
ln [cos x/(1 - sen x)]
y = arcsen x
y’ = 1/(1 – x2)½
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
coshx
y = cosh x
y’ = senh x
senh x
y = tgh x
y’ = sech2x
ln cosh x
y = cotgh x
y’ = -cosech2x
ln senh x
y = sech x
y’ = -sechx.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 = exy’ = ex
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
u.dv + v.duy = u/v
y’ = (u’.v – v’.u)/v2
7
y = uv
y’ = uv.(v’.lnu + v.u’/u)
8
y = lnuv
y’ = (v’.u.lnu – u’.v.lnv)/v.u.ln2u
9