1. TABLA DE DERIVADAS
TABLA DE DERIVADAS
FUNCIÓN FUNCIÓN DERIVADA FUNCIÓN FUNCIÓN DERIVADA
a 0 sen x cos x
x 1 sen u u' cos u
x2 2x cos x − senx
xm m ⋅ x m−1 cos u − u' senu
1
f ( x ) + g( x ) f ' ( x ) + g' ( x ) tgx 2
= 1 + tg 2 x
cos x
u'
k.f(x) k.f' (x) tgu
cos 2 u
−1
f ( x ) ⋅ g( x ) f ' ( x ) ⋅ g( x ) + f ( x ) ⋅ g' ( x ) cot gx 2
= −(1 + cot g 2 x )
sen x
f (x) f ' ( x ) ⋅ g( x ) − f ( x ) ⋅ g' ( x ) − u'
cot g u = −(1 + cot g 2 u) ⋅ u'
g( x ) g2 ( x ) 2
sen u
1 − f ' (x)
sec x tg x ⋅ sec x
f(x) f 2 (x)
(f o g)( x ) f ' (g(x )) ⋅ g' (x ) sec u u' ⋅ tg u ⋅ sec u
um m ⋅ um−1 ⋅ u' cos ec x − cot g x ⋅ cos ec x
1
ln x cos ec u − u'⋅ cot g u ⋅ cos ec u
x
u' 1
ln u arc sen x
u 1− x 2
ln x 1 u'
lga x = arc sen u
ln a x ln a 1− u2
u' −1
lga u arc cos x
u ln a 1− x 2
− u'
ex ex arc cos u
1− u2
1
eu u' e u arc tg x
1+ x 2
u'
ax a x . ln a arc tg u
1+ u2
−1
au a u .ln a u' arc ctg x
1+ x 2
⎛ v.u' ⎞ − u'
uv u v ⎜ v' ln u + ⎟ arc ctg u
⎝ u ⎠ 1+ u2
a,k ,m son constantes u,v,f,g,son funciones de la variable x

2. FÓRMULAS DE TRIGONOMETRIA
FÓRMULAS DE TRIGONOMETRIA
cat. opuesto cat. adyacente cat. opuesto sen α
senα = cos α = tgα = =
hipotenusa hipotenusa cat. adyacente cos α
1 1 1
cos ecα = sec α = tgα =
sen α cos α cot g α
sen 2 α + cos 2 α = 1 1 + tg 2 α = sec 2 α 1 + cot g2 α = cos ec 2 α
sen(α + β) = senα ⋅ cos β + cos α ⋅ senβ α 1 − cos α
sen 2α = 2 ⋅ sen α ⋅ cos α =±
sen(α − β) = senα ⋅ cos β − cos α ⋅ senβ
sen
2 2
cos(α + β ) = cos α ⋅ cos β − senα ⋅ senβ cos 2α = cos 2 α − sen 2 α α 1 + cos α
=±
cos(α − β ) = cos α ⋅ cos β + senα ⋅ senβ
cos
2 2
tgα + tgβ 2tgα α 1 − cos α
tg(α + β) = tg2α = =± tg
1 − tgα ⋅ tgβ 1 − tg 2 α 2 1 + cos α
A +B A −B A +B A −B
senA + 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
a b c (R=radio de la
Teorema de los senos: senA = senB = senC = 2R circunferencia circunscrita
al triángulo ABC)
Teorema del coseno: a 2 = b 2 + c 2 − 2 ⋅ b ⋅ c ⋅ cos A
1 1 a ⋅b ⋅c
Área de un triángulo ABC: S= b ⋅ hb = b ⋅ a ⋅ senC S=
2 2 4 ⋅R
a+b+c
S = p(p − a )(p − b )(p − c )
Fórmula de Herón:
donde p=
(p es el semiperímetro del triángulo) 2
FÓRMULAS DE LOGARITMOS
FÓRMULAS DE LOGARITMOS
loga N = b ⇔ a b = N a>0 loga M ⋅ N = loga M + loga N
M
loga a = 1 loga = loga M − loga N
N
loga 1 = 0 loga MN = N ⋅ loga M
logb M
loga a m = m log a M =
logb a
NOTA :
Si a = 10 → loga N = log N → (log aritmos decimales ) n
⎛ 1⎞
Si a = e → loga N = ln N → (log aritmos neperianos) e = lim ⎜1 + ⎟ = 2'718281....
n→ +∞
⎝ n⎠