Derivadas

TABLA DE DERIVADAS
SUMA Y RESTA

y = f(x) + g(x)

y´= f´(x) + g´(x)

PRODUCTO POR UN
y = k · f(x)
NÚMERO
PRODUCTO

y = f(x) · g(x)

COCIENTEy=

y´= k · f´(x)

REGLA DE LA
CADENA

y´= f´(x) · g(x) + f(x) · g´(x)

f (x)
g(x )

y´=

y = f[g(x)]

( g(x )) 2

y´= f´[g(x)] · g´(x)

y= xn
POTENCIAS

f ´(x ) ⋅ g ( x ) − f ( x ) ⋅ g´(x )

y´= n · xn–1

y=k
y=x

y´= 0
y´= 1

y=

x

y´=

1
2x

y = [f(x)]n

y=

f (x)y´= n · [f(x)]n–1 · f´(x)

y´=

1
2 f (x)

⋅ f ´(x )

y = ex

y´= ex

y = ef(x)

y = ef(x) · f´(x)

y = ax

y´= ax · ln a

y = af(x)y´= af(x) · ln a · f´(x)

y = ln x

y´=

y = ln f(x)

y´=

EXPONENCIALES

LOGARÍTMICAS
y = loga x

1
x
11
y´= ⋅
x ln a

y = loga f(x)

1⋅ f ´(x )
f (x)
11
⋅ f ´(x )
y´= ⋅
x ln a

y = sen x

y´= cos x

y = sen f(x)

y´= cos f(x) · f´(x)

y = cos x

y´= –sen x

y = cos f(x)y´= –sen f(x) · f´(x)

y = tg x

TRIGONOMÉTRICAS

y = cotg x

y´= 1 + tg2x
y´= sec2 x
y = tg f(x)
1
y´=
cos 2 x
y´= –1 – cotg2x
y´= –cosec2 x
y =tg f(x)
−1
y´=
sen 2 x

y = arcsen x

y´=

y = arccos x

y´=

y = arctg x

1
1− x2
−1

1− x2
1
y´=
1+ x2

y = arcsen f(x)

y´= [1 +tg2 f(x)] · f´(x)
y´= sec2 f(x) · f´(x)
1
⋅ f´(x)
y´=
2
cos f (x)
y´= [–1 – cotg2 f(x)] · f´(x)
y´= –cosec2 f(x) · f´(x)
−1
⋅ f´(x)
y´=
sen 2 f (x)1
⋅ f´(x)
y´=
1 − (f (x)) 2

y = arccos f(x)

y´=

y = arctg f(x)

y´=

−1
1 − (f (x)) 2

⋅ f´(x)

1
⋅ f´(x)
1 + (f (x)) 2