Tabla de derivadas

Contenido
Tabla de Derivadas.
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 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/cos ² 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 xy´ = 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 x
y = sh x y´ = ch x ch x
y = ch xy´ = sh x sh x
y = th x y´ = sech ²x log ch x
y = coth x y´ = -cosech ²x log sh x
y = sech x y´ = -sech x.th x
y = cosech xy´ = -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 = axy´ = ax.log a ax/log a
y = xx y´ = xx.(log x + 1)
y = eu y´ = 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
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