derivadas de las funciones más usuales

DERIVADAS DE LAS FUNCIONES USUALES
FUNCIONES
y = k , k ≡ cte.
y=x
y=u+v
y =u⋅v
y=
u
v
DERIVADAS
y' = 0
y' = 1
y ' = u' + v '
y ' = u '⋅ v + u ⋅ v '
y' =
FUNCIONES
DERIVADAS
u = u ( x) , v = v( x) , es decir, se trata de funciones.
u '⋅ v ' − v '⋅ u '
v2
y = xn , n ∈ ℜ
y ' = n ⋅ x n −1
y = un
y ' = n ⋅ u n −1 ⋅ u '
y=n x
y' =
y=n u
y' =
y = Ln ( x )
y' =
1
x
1
y ' = ⋅ log a e
x
y = Ln ( u )
1
u'
⋅u' =
u
u
1
y ' = ⋅ u ' ⋅ log a e
u
y = ex
y' = e x
y = eu
y ' = eu ⋅ u '
y = ax
y ' = a x ⋅ Ln a
y = au
y ' = a u ⋅ u ' ⋅ Ln a
y = sen ( x )
y ' = cos ( x )
y = sen ( u )
y ' = cos ( u ) ⋅ u '
y = cos ( x )
y ' = − sen ( x )
y = cos ( u )
y ' = − sen ( u ) ⋅ u '
y = tg x
y' =
y = tg ( u )
y' =
y = co tg x
y' = −
y = cotg ( u )
y' = −
y = sec x
y ' = sec ( x ) ⋅ tg ( x )
y = sec ( u )
y ' = sec ( u ) ⋅ tg ( u ) ⋅ u '
y = cose c x
y ' = − cosec ( x ) ⋅ cotg ( x )
y = cosec ( u )
y ' = − cosec ( u ) ⋅ cotg ( u ) ⋅ u '
y = log a x
y = arc sen x
y' =
y = arccos x
y' =
y = arc tg x
y' =
1
n ⋅ n x n −1
1
cos
2
( x)
1
sen
2
( x)
1
1 − x2
−1
1 − x2
1
1 + x2
= 1 + tg 2 ( x )
y = log a ( u )
⋅u'
n ⋅ n u n −1
y' =
y = arcsen ( u )
y' =
y = arc cos ( u )
y' =
y = arctg ( u )
1
y' =
1
cos 2 ( u )
⋅u'
1
sen 2 ( u )
1
1 − u2
−1
1 − u2
⋅u'
⋅u'
⋅u'
1
⋅u'
1 + u2