Formulario de derivadas
1. 2. 3.
Tabla de derivadas Matemáticas 27. 28.
y=a
y′ = 0
y = sec x
y = a ⋅ xn
y ′ = n ⋅ a ⋅ x n -1 y ′ = n ⋅ ( f ) n−1 ⋅ f ′ 1 y′ = x f′ y′ = f 1 y ′ = ⋅ log a(e) x f′ y′ = ⋅ log a (e) f
y′ = a x ⋅ L(a ) y′ = f ′ ⋅ a ⋅ L(a )
f
y = ( f )n 4. y = L(x)
5. 6. 7.
y = sec( f ) 29. y = cos ecx
30. 31.
y = cos ec( f )
y = arcsenx
y ′ = sec x ⋅ tgxy′ = f ′ ⋅ sec( f ) ⋅ tg ( f ) y′ = − cos ecx ⋅ cot gx y′ = − f ′ ⋅ cos ec( f ) ⋅ cot g ( f )
y = L(f )
y = log a ( x)
y = log a ( f ) y = ax y=a
f
y′ =
y′ =
1 1 − x2
f′ 1 − (f )2
32.33.
y = arcsen( f )
y = arccos x
y′ = y′ =
y′ = y′ =
−1 1 − x2 − f′ 1− ( f ) 1 1 + x2 f′
2
8. 9. 10. 11. 12.
34.
y = arccos( f )
y = ex y = ef
y′ = e x y′ = f ′ ⋅ e f f′ y′ =n ⋅ n ( f ) n −1 y′ = f ′ ⋅ g + g ′ ⋅ f f ′ ⋅ g − g′ ⋅ f y′ = g2 y′ = cos x y′ = f ′ ⋅ cos( f )
35. y = arctgx 36.
y=n f
y = arctg ( f )
y = f ⋅g f 14. y = g 15. y = senx
13. 16. 17.37. y = arc cot gx 38.
y = arc cot g ( f )
y = sen n ( f ) 18. y = cosx
19. 20. 21. 22.
y = sen( f )
39. y = arc sec x
y = cos n ( f ) y = tgx
y = cos( f )
y′ = -f ′ ⋅ sen (f )y′ = n ⋅ sen n −1 (f ) ⋅ f ′ ⋅ cos(f ) y′ = − senx
y′ = − n ⋅ cos n −1 ( f ) ⋅ f ′ ⋅ sen( f
1+ ( f ) −1 y′ = 1 + x2 − f′ y′ = 2 1+ ( f ) 1 y′ = x ⋅ x2 − 1
2
40.
y = arc sec( f )
y′ =y′ =
f′ f ⋅
( f )2 − 1
−1
41. y = arccos ecx
y′ =
y = tg ( f )
y = tg n ( f )
y = cot gx
1 = 1 + tg 2 x 2 cos x f′ y′ = = f ′ ⋅ 1 + tg 2 ( f 2 cos ( f )
42.
y = arccos ec( f )x ⋅ x2 − 1
y′ =
− f′ f ⋅
[
( f )2 − 1
g 43. Derivación logarítmica:- y = (f )
23. 24. 25. 26.
y′ = n ⋅ tg n −1 ( f ) ⋅ y′ =
y′ =
f′ cos 2 ( f )
y = cot g ( f )
y = cotg n ( f )
−1 = − 1 + cot g 2 x 2 sen x
(
)
sen 2 (f )
f′ sen 2 ( f )
−f ′
1º) Tomar L (logaritmos neperianos) en ambos miembros: Ly = g ⋅ Lf . 2º) Derivar en ambos miembros:...
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