tema variado

Tabla de Derivadas e Integrales
Función
Derivada
Integral
y = c
y´ = 0
c.x
y = c.x
y´ = c
c.x ²/2
y = xn
y´ =n.xn-1
x(n + 1)/(n + 1)
y = x-n
y´ = -n/x(x + 1)
-x-(n + 1)/(n + 1)
y = x½
y´ = 1/(2.√x)
x3/2/(3/2)
y = xa/b
y´ = x(a/b- 1)/(b/a)

y = 1/x
y´ = -1/x ²
log x
y = sin x
y´ = cos x
-cos x
y = cos x
y´ = -sin x
sin x
y = tan x
y´ = 1/cos² x
-log cos x
y = cotan x
y´ = -1/sin ² x
log sin x
y = sec x
y´ = sin x/cos ² x
y´ = log (tg x/2)
y = cosec x
y´ =-cos x/sin ² x
y´ = log [cos x/(1 - sen x)]
y = arcsen x


y = arccos x


y = arctg x
y´ = 1/(1 + x ²)
x.arctg x -[log (1 + x ²)}/2
y = arccotan x
y´ = -1/(1 + x ²)
x.arccotg x + [log (1 + x ²)}/2
y = arcsec x

 
y = arccosec xy = sh x
y´ = ch x
ch x
y = ch x
y´ = sh x
sh x
y = th x
y´ = sech ²x
log ch x
y = coth x
y´ = -cosech ²x
log sh xy = sech x
y´ = -sech x.th x
 
y = cosech x
y´ = -cosech x.coth x

y = log x
y´ = 1/x
x.(log x - 1)
y = logax
y´ =1/x.log a
x.(log a x - 1/log a)
y = ex
y´ = ex
ex
y = ax
y´ = ax.log a
ax/log a
y = xx
y´ = xx.(log x + 1)
 
y = euy´ = eu.u´

y = u.v
y´ = u´.v + v´.u
∫u.dv + ∫v.du
y = u/v
y´ = (u´.v - u.v´)/v ²
 
y = uv


y = loguv