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TABLA DE DERIVADAS TABLA DE DERIVADAS
FUNCIÓN FUNCIÓN DERIVADA FUNCIÓN FUNCIÓN DERIVADA

a
x

0

sen x
sen u

cos x
u' cos u

1
2x m ⋅ x m−1

x2

cos x cos u

− senx
− u' senuxm

f ( x ) + g( x )
k.f(x) f ( x ) ⋅ g( x )
f (x) g( x ) 1 f(x)

f ' ( x ) + g' ( x )
k.f' (x) f ' ( x ) ⋅ g( x ) + f ( x ) ⋅ g' ( x )
f ' ( x ) ⋅ g( x ) − f ( x ) ⋅ g' ( x ) g2 ( x ) − f '(x) f 2 (x)
f ' (g(x )) ⋅ g' (x )

tgx
tgu cot gx
cot g u
sec x

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
tg x ⋅ sec x u' ⋅ tg u⋅ sec u − cot g x ⋅ cos ec x

(f o g)( x )
um

sec u cos ec x

m ⋅ um−1 ⋅ u' 1 x u' u ln x ln a 1 x ln a u' u ln a ex u' e u a x . ln a a u .ln a u' v.u' ⎞ ⎛ u v ⎜ v' ln u + ⎟ u ⎠ ⎝

ln x
ln ulga x = lga u ex eu ax au uv

cos ec u
arc sen x
arc sen u

− u'⋅ cot g u ⋅ cos ec u
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

arc cos x arc cos uarc tg x arc tg u arc ctg x arc ctg u

a,k ,m son constantes

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

FÓRMULAS DE TRIGONOMETRIA FÓRMULAS DE TRIGONOMETRIA
cat. opuesto hipotenusa 1 cos ecα = senα senα =
sen(α + β) = senα ⋅ cos β + cos α ⋅ senβ sen(α − β) = senα ⋅ cos β − cos α ⋅ senβ

cos α =

cat. adyacente hipotenusa 1 sec α = cos α

tgα =

cat. opuesto sen α = cat. adyacente cos α1 tgα = cot g α
α 1 − cos α =± 2 2 α 1 + cos α =± 2 2

sen 2 α + cos 2 α = 1

1 + tg 2 α = sec 2 α

1 + cot g2 α = cos ec 2 α
sen cos tg

sen 2α = 2 ⋅ sen α ⋅ cos α cos 2α = cos 2 α − sen 2α
tg2α = 2tgα 1 − tg 2 α

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

α 1 − cos α =± 2 1 + cos α A +B A +B A −B A −BsenA + senB = 2 ⋅ sen ⋅ cos cos A + cos B = 2 ⋅ cos ⋅ cos 2 2 2 2 A +B A +B A −B A −B senA − senB = 2 ⋅ cos ⋅ sen cos A − cos B = −2 ⋅ sen ⋅ sen 2 2 2 2 (R=radio de la a b c circunferencia...