Dbujo

1.- f= (5x2-2x) (2x-3)

U= 5x2 - 2x f`= (5x2 - 2x) dv/dx (2x – 3) + (2x – 3) du/dx (5x2 - 2x)
du= 10x - 2dx f`= (5x2 - 2x) (2) + 2x - 3 (10x - 2dx)V= 2x - 3 f`= 10x2 - 4x + 20x2 - 4x - 30x +6
dv= 2dx f`= 30x2 - 38x + 6

( ) 38x2 - 30x + 6 (x) 30x2 - 38x + 6 ( ) -30x + 38x2 + 6 ( ) 30x2 - 38x + 62.- f= (x2 + 3x) (4 + x3)

u= x2 + 3x f`= (x2 + 3x) dv/dx (4 + x3) + (4 + x3) du/dx (x2 + 3x)
du= 2x + 3dx f`= (x2 + 3x) (3x2) + (4 + x3) (2x + 3)v= 4 + x3 f`= 3x4 + 9x3 + 8x + 2x4 + 12 + 3x3
dv= 3x2dx f`= 5x4 + 11x3 + 8x + 12

( ) 5x3 + 11x3 + 8x2 + 12 ( ) 4x5 + 3x11 +x + 12 (x) 5x4 +11x3 + 8x + 12 ( ) 5x4 - 11x3 - 8x - 12

Ejercicios del libro de Leithold
Pag. 131
Ejercicio 3
G(x)= 1-2x-x2
Y`= -2-2x
Y`= -2x-2

Ejercicio 28
G(x)=(2x+1 / 3x+4)
d/dx (u/v)= u(d/dx v) – v(d/dx u)/ v2
Y`= (2x+1(d/dx 3x+4) )– (3x+4(d/dx 2x+1)) / (3x+4)2
Y`= ((2x+1)(3)) – ((3x+4)(2)) / (9y2 + 24y + 16)
Y`= 11 / (9y2+ 24y + 16)

Pag. 160
Ejercicio 17
d/dx= (cos x) (cot x)
d/dx (uv)= u d/dx v + v d/dx u
y`= cosx d/dx cotx + cotx d/dx cosx
y`= cosx d/dx cotx +(-senx)(cotx)
y`= cos x (-csc2 x) – cosx

Pag. 483
Ejercicio 33
g(x)= tan-1 2x | |
| d/dx tan-1 u= 1/1+u2 (du/dx) |
g(x)`= (1/1 + (2x)2 )(du/dx) (2x) | |
g(x)`=(1/1 + 4x2) (2) | |
g(x)`=2/1 + 4x2 | |

Ejercicio del libro de James Stewart
Pag.
Y=xeex | |
u=x | v=eex |
u`=1 | v`=eex+1 |
| |
v du/dx + udv/dx | |
eex ( d/dx (x))+ x(d/dx (eex)) | |
x (eex ( d/dx (ex))) + eex (d/dx (x)) | |
eex x (e(d/dx(x)) + eex | |
eex+1 x + eex | |
| eex (ex ) |