Tabla de Derivadas e Integrales

Función	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’ = cos x	-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’ = sen x/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	cosh x
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’ = -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’ = 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	òu.dv + òv.du
y = 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