Tabla de derivadas

Derivadas directas de las principales funciones
Función	Derivada
y = c	y' = 0
y = c·x	y' = c
y = xⁿ	y' = n·x^{n - 1}
y = x^-n	y' = -n/x^{(x + 1)}
y = x^½	y' = 1/(2·√x)
y = x^a/b	y' = x^{(a/b - 1)}/(b/a)
y = 1/x	y' = -1/x²
y = sen x	y' = cos x
y = cos x	y' = -sen x
y = tg x	y' = 1/cos² x
y = cotg x	y' = -1/sen² x
y = sec x	y' = sen x/cos² x
y = cosec x	y' = -cos x/sen² x
y = arcsen x	y' = 1÷(√1 - x²)
y = arccos x	y' = -1÷(√1 - x²)
y = arctg x	y' = 1/(1 + x²)
y = arccotg x	y' = -1/(1 + x²)
y = arcsec x	y' = 1÷(x·√x² - 1)
y = arccosec x	y' = -1÷(x·√x² - 1)
y = sh x	y' = ch x
y = ch x	y' = sh x
y = th x	y' = sech²x
y = coth x	y' = -cosech²x
y = sech x	y' = -sech x·th x
y = cosech x	y' = -cosech x·coth x
y = ln x	y' = 1/x
y = log x	y' = 1/x
y = log_a x	y' = 1/x·log a
y = e^x	y' = e^x·ln e = e^x
y = a^x	y' = a^x·log a
y = x^x	y' = x^x·(log x + 1) = x^x·(ln x + 1)
y = e^u	y' = e^u·u'
y = u·v	y' = u'·v + v'·u
y = u/v	y' = (u'·v - u·v')/v²
y = u^v	y' = u^v·[v'·log u + u'·v/u]
y = log_u v	y' = (u·v'·log u - u'·v·log v)÷(u·v·log² u)

Autor: Ricardo Santiago Netto. Argentina