Calculo

EJERCICIOS DE CALCULO DIFERENCIAL

* Aplicando la definición de diferencial, calcular las diferenciales de las siguientes funciones:

1. Y= 3x4
dy = 12x3
dx
dy= 12x3dx

2. Y=2x3-3x2+8x-1
dy = 6x2-6x+8
dx
dy= 6x2-6x+8dx

3. Y=
Y= (1-4x)1/2
dy = ½ (1-4x) -1/2 (-4)
dx
dy = -4 = -2
dx 2(1-4x)1/2
dy = -2dx


4. Y= Sen2x
dy = cos 2x( 2)
dx
dy = 2 cos2x
dx
dy= 2 cos2xdx

5. Y= Cos23x
Y= ½ [1+Cos2(3x)]
Y= ½ (1+Cos6x)
Y= ½ + ½ Cos6xdy = ½ (-Sen 6x) (6)
dx
dy = 3 ( -Sen6x)
dx
dy = -3Sen6x
dx
dy= -3Sen6xdx

6. Y= 1 - x
X2
dy = x2(-1) - (1-x )(2x) = -x2-2x+2x2 = -2x + x2 = x(-2+x)
dx x4 x4 x4 x4
dy = -2+x
dx x3
dy= x-2 dx
x37. Y= 2Sec3x
dy = 2 ( sec3x . tg3x)(3)
dx
dy = 6sec3x . tg3x
dx
dy = 6sec3x . tg3xdx

8. Y= arc cos 4x
dy = - 1 ( 4)
dx
dy = - 4
dx
dy =- 4
dx
dy = - 4 dx


9. Y= arc tag (1-x)
dy = 1 (-1)
dx 1+(1-x)2
dy = -1 = -1 = -1 .
dx 1+(1-x)21+ 1-2x+x2 2-2x+x2
dy = -1 dx
2-2x+x2
10. Y= arc csc
dy = -1 (1/2 x-1/2)
dx ()
dy = -1
dx 2()
dy =-1
dx 2x ()
dy = -1 dx
2x ()
11. Hallar el incremento de área de un cuadrado de lado 8m al aumentar el lado 5mm.
L= 8 m A= 0.005mA= L2
dA = 2L
dL

dA= 2LdL
dA=2(8m)(0.005m)
dA= 0.08m2

12. Hallar el incremento de volumen de un cubo de lado 4.5m al aumentar de lado 0.004m
L= 4.5m A= 0.004m

A= L3...