Movimiento angular en un plano

Universidad Autónoma de Chihuahua

Facultad de ingeniería
Calculo Diferencial e Integral
Derivada implícita y de orden superior

Pedro Iván Corral Armendáriz
244953“1HW2”


Derive de forma implícita las siguientes ecuaciones: (encuentre y’)

1. 3x3 + 4y3 + 8 = 0
9x2 + 12y2y’ = 0
12y2y’ = -9x2
y’ =

2. xy2 -x2y + x2 + 2y2 = 0(x2yy’ + y2) – (x2y’ + y2x) + 2x + 4yy’ = 0
x2yy’ + y2 – x2y’ – y2x + 2x +4yy’ = 0
x2yy’ – x2y’ + 4yy’ = -y2 + y2x – 2x
y’(x2y – x2 + 4y) =-y2 + y2x – 2x
y’ =

3. x = y - y7
y – y7 – x = 0
y’ – 7y6y’ -1 = 0
y’(1-7y6) = 1
y’ =

4. x4 y3 - 3xy = 60
(x43y2y’ + 4x3y3) – 3(xy’ + y) = 60x43y2y’ + 4x3y3 – 3xy’ – 3y = 60
x43y2y’ – 3xy’ = 60 – 4x3y3 +3y
y’(x43y2 – 3x) = 60 – 4x3y3 + 3y
y’ =

5. x3 – y3 = 4xy
x3 – y3 – 4xy = 0
3x2 – 3y2y’ – 4(xy’ + y) = 03x2 – 3y2y’ – 4xy’ + 4y = 0
-3x2y’ – 4xy’ = -3x2 – 4y
y’ =

6. x2 + y – y2 = 5
2x + y’ – 2yy’ = 0
y’ – 2yy’ = -2x
y’(1 – 2y) = -2x
y’ =

Hallar lascuatro primeras derivadas de:

a) 8x – 3
y’ = 8
y’’ = 0
y’’’ = 0
y4 = 0

b) 8x2 – 11x + 2
y’ = 16x – 11
y’’ = 16
y’’’ = 0
y4 = 0

c) 8x3 + 7x2 – x + 9y’ = 24x2 + 14x
y’’ = 48x + 14
y’’’ = 48
y4 = 0

d) x4 – 13x3 + 5x2 + 3x – 2
y’ = 4x3 – 39x2 + 10x + 3
y’’ = 12x2 – 78x + 10
y’’’ = 24x – 78
y4 = 24

e) x5/2
y’ =x 3/2

y’’ = x 1/2

y’’’ = x-2/2

y4 = x-4/2

Obtener la segunda derivada de:

i) y =

y’ =

y’ =

y’’ =

y’’ =

y’’ =

ii)y = x3 +

y’ = x3 + x-3

y’ = 3x2 -3x-4

y’’ = 6x -12x-5

y’’ = 6x -

y’’ =

iii) y =

y’ =

y’ =

y’ =

y’’ =

y’’ =

y’’...