x - IES Gabriela Mistral

TABLA DE DERIVADAS
FUNCIÓN
DERIVADA
EJEMPLO
y=k
y´= 0
y =8
y´= 0
y = xn
y´= nx n −1
y = x5
y´= 5 x 4
y´= n ⋅ u n −1 ⋅ u´
y = (2 x + 1) 3
y´= 3( 2 x + 1) 2 ⋅ 2
y = 5x
y´=
y = un
(u =
f (x) )
y= u
y´=
y= u
y´=
y = eu
u'
2 u
u´
y´=
5
2 5x
6x
y = 3x
2
y´= u´⋅e u
y = e3x
+1
y = au
y´= u´⋅a u ⋅ La
y = 53 x−4
y = Lu
y´=
u´
u
y = L x2 + 7x
)
y´=
2x + 7
x2 + 7x
y = log a u
y´=
u´
⋅ log a e
u
y = log 2 (5 x + 7 )
y´=
5
⋅ log 2 e
5x + 7
y = sen(u )
y´= u´⋅ cos(u )
y = sen5 x
y´= 5 ⋅ cos 5 x
y = cos(u )
y´= −u´⋅sen(u )
y = cos 3x 2
y´= −6 x ⋅ sen3 x 2
y = tg (u )
y´= u´⋅ sec 2 (u )
y = tg 7 x
y´= 7 ⋅ sec 2 7 x
m
mm u m −1
5
2
( )
4
5 ⋅ 5 3x 2
y´= 6 x ⋅ e 3 x
2
+1
y´= 3 ⋅ 5 3 x −4 ⋅ L5
(
REGLAS DE DERIVACIÓN
y = k ⋅u
y´= k ⋅ u´
y = 3x 5
y´= 15 x 4
y =u+v−w
y´= u´+ v´− w´
y = 3x 2 − 2 x + 5
y = 6x − 2
y = u ⋅v
y´= u´⋅v + u ⋅ v´
y = x 2 ⋅ cos x
y´= 2 x cos x − x 2 senx
u
y=
v
u´⋅v − u ⋅ v´
y´=
v2
2x 2
y= 3
x −1
[ f (g (x) )]′
f ´(g ( x) ) ⋅ g´(x)
y = 2x 2 + 1
(
y´=
)
5
(
)
4 x x 3 − 1 − 2 x 2 ⋅ 3x 2
(
(x
)
−1
3
)
4
2
y´= 5 2 x 2 + 1 ⋅ 4 x