Ingenieria mecanica

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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:...