TABLA DE DERIVADAS

4,314 views

Published on

0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
4,314
On SlideShare
0
From Embeds
0
Number of Embeds
133
Actions
Shares
0
Downloads
65
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

TABLA DE DERIVADAS

  1. 1. TABLA DE DERIVADAS TABLA DE DERIVADAS FUNCIÓN FUNCIÓN DERIVADA FUNCIÓN FUNCIÓN DERIVADAa 0 sen x cos xx 1 sen u u cos ux2 2x cos x − senxxm m ⋅ x m−1 cos u − u senu 1f ( x ) + g( x ) f ( x ) + g ( x ) tgx 2 = 1 + tg 2 x cos x uk.f(x) k.f (x) tgu cos 2 u −1f ( x ) ⋅ g( x ) f ( x ) ⋅ g( x ) + f ( x ) ⋅ g ( x ) cot gx 2 = −(1 + cot g 2 x ) sen xf (x) f ( x ) ⋅ g( x ) − f ( x ) ⋅ g ( x ) − u cot g u = −(1 + cot g 2 u) ⋅ ug( x ) g2 ( x ) 2 sen u 1 − f (x) sec x tg x ⋅ sec xf(x) f 2 (x)(f o g)( x ) f (g(x )) ⋅ g (x ) sec u u ⋅ tg u ⋅ sec uum m ⋅ um−1 ⋅ u cos ec x − cot g x ⋅ cos ec x 1ln x cos ec u − u⋅ cot g u ⋅ cos ec u x u 1ln u arc sen x u 1− x 2 ln x 1 ulga x = arc sen u ln a x ln a 1− u2 u −1lga u arc cos x u ln a 1− x 2 − uex ex arc cos u 1− u2 1eu u e u arc tg x 1+ x 2 uax a x . ln a arc tg u 1+ u2 −1au a u .ln a u arc ctg x 1+ x 2 ⎛ v.u ⎞ − uuv 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. 2. FÓRMULAS DE TRIGONOMETRIA FÓRMULAS DE TRIGONOMETRIA cat. opuesto cat. adyacente cat. opuesto sen αsenα = cos α = tgα = = hipotenusa hipotenusa cat. adyacente cos α 1 1 1cos ecα = sec α = tgα = sen α cos α cot g αsen 2 α + cos 2 α = 1 1 + tg 2 α = sec 2 α 1 + cot g2 α = cos ec 2 αsen(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 2cos(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 αtg(α + β) = tg2α = =± tg 1 − tgα ⋅ tgβ 1 − tg 2 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 −BsenA − 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 + ⎟ = 2718281.... n→ +∞ ⎝ n⎠

×