Tabla de derivadas

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AB
BL
LA
AD
DE
ED
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RIIV
VA
AD
DA
AS
S
FUNCIÓN

FUNCIÓN DERIVADA

FUNCIÓN

FUNCIÓN DERIVADA

a

0

sen x

cos x

x

1

sen u

u' cos u

x2

2xcos x

− senx

xm

m ⋅ x m−1

cos u

− u' senu

f ( x ) + g( x )

f ' ( x ) + g' ( x )

tgx

k.f(x)

k.f' (x)

tgu

f ( x ) ⋅ g( x )

f ' ( x ) ⋅ g( x ) + f ( x ) ⋅ g' ( x )cot gx

f (x)
g( x )
1
f(x)

f ' ( x ) ⋅ g( x ) − f ( x ) ⋅ g' ( x )
g2 ( x )
− f ' (x)
f 2 (x)

(f o g)( x )
um

ln x
ln u

sec x

tg x ⋅ sec x

f ' (g(x )) ⋅ g' (x )

sec uu' ⋅ tg u ⋅ sec u

m ⋅ um−1 ⋅ u'

cos ec x

− cot g x ⋅ cos ec x

1
x
u'
u

cos ec u

− u'⋅ cot g u ⋅ cos ec u

arc sen x

lga u

1
x ln a
u'
u ln a

ex

ex

arc cos ueu

u' e u

arc tg x

ax

a x . ln a

arc tg u

au

a u .ln a u'

arc ctg x

uv

v.u' ⎞
⎛
u v ⎜ v' ln u +
⎟
u ⎠
⎝

arc ctg u

lga x =

ln x
ln a

cot g u

1
=1 + tg 2 x
2
cos x
u'
cos 2 u
−1
= −(1 + cot g 2 x )
2
sen x
− u'
= −(1 + cot g 2 u) ⋅ u'
2
sen u

a,k ,m son constantes

arc sen u

arc cos x

1
1− x 2
u'
1− u2
−1
1− x 2
−u'
1− u2
1
1+ x 2
u'
1+ u2
−1
1+ x 2
− u'
1+ u2

u,v,f,g,son funciones de la variable x

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RIIA
A
senα =cat. opuesto
hipotenusa
1
cos ecα =
sen α

cos α =

cat. adyacente
hipotenusa
1
sec α =
cos α

sen 2 α + cos 2 α = 1

1 + tg 2 α = sec 2 α

sen(α + β) = senα ⋅ cos β + cos α ⋅senβ
sen(α − β) = senα ⋅ cos β − cos α ⋅ senβ

cos(α + β ) = cos α ⋅ cos β − senα ⋅ senβ
cos(α − β ) = cos α ⋅ cos β + senα ⋅ senβ
tgα + tgβ
tg(α + β) =
1 − tgα ⋅ tgβ

cat. opuesto
sen α
=cat. adyacente cos α
1
tgα =
cot g α

tgα =

1 + cot g2 α = cos ec 2 α

sen 2α = 2 ⋅ sen α ⋅ cos α
cos 2α = cos 2 α − sen 2 α
2tgα
1 − tg 2 α

sen

α
1 − cos α
=±
2
2

cos

α...