Taller 8

TALLER No. 8

1

x5 5x 4

2

=x =3

3 1

2

( x)2

1

2

3 1 t3 t 3 (0 ) −1(3t 2 )

(t ) 3

2

t 3 −3t 2 t6

4

4 u4 u 4 ( 0 ) −4(4u 3 )

(u ) 4

2

u 4 −16u 3 u8 1 5u 5 5u 5 (0 ) −1(25 u 4 )

5

(5u ) 5

2

−25 u 4 5u 10

6 x7 7 7(7 x 6 ) −x 7 ( 0 ) 72 49 x 6 49

7

1 3

x

x 2

3

2

=

1 x

2

3

− (0 ) −1 2 3 x 3   1



 x 

2



2

3

  

−1 −1 0 −1 −2  2 3 x 3   x 3   3  =   4 4 3 3 x x

8 2 x −x 3 2 −3 x 2

9 4 x 3 −3 x 2 +7 12 x 2 −6 x

10 5 −2 x 2 + x 4 −4 x +4 x 3

11 3 x 4 −7 x 3 +5 x 2 +8 12 x 3 −21x 2 +10 x

12

1 x ( x  0 ) −1(1)  + } x2  

4 x 3 +2 + 12 x 2

0 −1 12 x 2 + 2   x   −1  12 x 2 + 2  x 

13

3 u2 u 2 (0 ) −3( 2u )  6u +  (u 2 )2    

3u 2 +

 −6u  6u + 4   u 

14 x 6

6 + 6 6 x 6 6 x 5 − x 6 (0 ) x 6 ( 0 ) −6 6 x 5 + 2 62 x6

(

)

( )

36 x −0 0 −36 x + 36 x 12 −36 x 5  36 x 5 +  x 12   36   5

15

(

5

1 x 0,6 x 0 , 6 (0 ) −1(0,6 x −0 , 4 ) 1,2 x 0 , 2 + ( x 0 , 6 )2 x 1, 2 +

0 −1,6 x −0 , 4 x 1, 2 1,6 x −0 , 4   +  x 1, 2   

1,2 x 0 , 2 + 1,2 x 0 , 2

)

16 x 0, 4 − x −0, 4

0,4 x −0, 6 −(−0,4 x −1, 4 )

17

x +

2 2x x

18

1

−1

2

=2 x

x

1

2

+

+2 x 2   =2 x   3 − + x 2     −1

2

2

2 x 1

1

2

2

+2 x

−1

2

1 7 +7 x + +7 x x7 7 x ( 0 ) −1(7 x 6 )  x (0 ) −7(1)  7 x 6 +  +7 +  7 2 x2   (x )     6 0 −7 x  0 −7  7 x 6 +  +7 + 2  49  x   x  x7 +

−7 x 6  −7  7 x 6 + 49  +7 + 2  x   x 

19 2 x 3 + 2 3 2 x 2 

2x 3x

20

3 1

2 t  2t

1

1

−1

2

2

−5 + −3 x 2    

2

2

−3

+2 x

2

t −3

2

1t

3 2 = 2 x 2  + 3   x 2 x 3 −   +2 x 2      3

2

3

=2

t

3

 −  t

1

−1

−3t

3

t −3

= 2 t 

3

1

t 2

−1   −3 t 3     

3

−4 − −1t 3    

21 2 x 5 2 +4 x 5 4 3x

22

3

x x 1

1

2

+5 x

x −3 1

1

3

3

3

−

1

1 x 1

x

−x x

−2

4

3

1

3

−1

=x

1

3

−1 x 

−1

3

−4 3  − − 1 3 x   

3

  

23 3 x 4 +( 2 x −1) 2

12 x 3 +2( 2 x −1)( 2 ) 12 x 3 +4( 2 x −1)

24 ( y −2 )( 2 y −3)

( y −2 )( 2 ) +( 2 y −3)(1) ( 2 y −4) +( 2 y −3)

25

26

( x −7 )( 2 x −9 ) ( x −7 )( 2 ) +( 2 x −9 )(1) ( 2 x −14 )( 2 x −9 ) 2

1  x +  x  1  x ( 0 ) −1(1)   2x + 1 +  x  x2   1  0 −1   2x + 1 +  x x2    1    −1  2x + 1 + 2  x    x 

27 (u +1)( 2u +1)

(u +1)( 2 ) +( 2u +1)(1) ( 2u +2 )( 2u +1)

28    

2

x +

1    x 

 12 1 x + 1  x 2 

2

2  1 −1 2   = x 2 +1 x          2

x 1 2 + x −1 2      2 x  

1

2 x  

1

2

2

(

1 x −3 2 + − 1 x 2    2 −1 +x 2    +x

−1

2

29

(t +1)(3t −1) 2 (t +1)2(3t −1)(3) +(3t −1) 2 (1) (t +1)6(3t −1) +(3t −1) 2 (t +1)(18t −6 ) +(3t −1) 2

30

(u −2) 3 2 3(u −2 ) (1) 2 3(u −2 )

)

−3

2

  

31

( x +2 ) 3 2 3( x +2 ) (1) 2 3( x +2 )

32 ( x +1)( x −1) 2

( x +1)2( x −1)(1) +( x −1) 2 (1) ( x +1)2( x −1) +( x −1) 2 ( x +1)( 2 x −2 ) +( x −1) 2

33  x +1 3  

x

 

 x +1  x (1) −( x +1)(1)  3   x2  x     2

 x +1  x −( x +1)  3    x2  x    2

34 2t −1 3   2t

 

 2t −1  2t ( 2 ) −( 2t −1)( 2 )  3   2t 2  2t     2

 2t −1  4t −( 4t −2 )  3   2t 2  2t     2

3 35  y +2 3  y −2      +  y   y     

 y +2   y (1) −( y +2 )(1)   y −2   y (1) −( y −2 )(1)  3  +3  2  y     y    y y2         2

2

 y +2   y −( y +2 )   y −2   y −( y −2 )  3  +3  2  y     y    y y2         2

36 2 y 2 +3 y −7 y

y ( 4 y +3) −(2 y 2 +3 y −7 )(1) y2

(4 y

2

+3 y ) −(2 y 2 +3 y −7 ) y2

4 y 2 +3 y −2 y 2 −3 y +7 y2 2 y 2 +7 y2

2

37

( x +1) 2 x 2 x[2( x +1)(1)] −( x +1) (1) x2 2 x[2( x +1)] −( x +1) x2 2 2 x ( x +1) −( x +1) 2 x

2 2 38 x −3 x +1 = x −3 x +1 1

x

x

1

2

( 2 x −3) −( x

x

2

2

[

−3 x +1) 1

( x ) − 2 (1) 1

2

]

2

1  x 2    

[

1 1 −1 2  2 x 2 −3 x 2   −( x −3 x +1) 1 2 ( x ) 2  

]

2

1  x 2    

39

3 3 t+ −1 t = t = t +3  t 2   1  t  t x 2 t ( 0 ) −3(1)  1 (t ) −3 2 (1) t + − 2  2 t   t+

[

]

[

0 −3  −3 t + 2  − 1 ( t ) 2 2 t   3  −3  1 t + 2  − (t ) − 2 2 t 

[

]

]

2 ( x −1) 2 40 ( x +1) + 2

x 2 2 x 2 [2( x +1) +2( x −1)] −( x +1) +( x −1) ( 2 x ) 4 x x 2 [( 2 x +2 ) +( 2 x −2 )] −(2 x 2 +2 x ) +( x −1) x4 2

41

( 2t

−( 2t −3) 4t 2 2 4t [2( 2t +3)( 2 ) +2( 2t −3)( 2 )] −( 2t +3) −( 2t −3) ( 4 ) 2 4t 2 2 4t [4( 2t +3) +4( 2t −3)] −(8t +12 ) −( 2t −3) 2 4t 2 2 4t [(8t +12 ) +(8t −12 )] −(8t +12 ) −( 2t −3) 2 4t 2 2 32t 2 +48t +(8t −12 ) −(8t +12 ) −( 2t −3) 4t 2

(

+3)

2

2

2

)

42

x 1, 6 x 2,3 x 2 , 3 (1,6 x 0 , 6 ) −x 1, 6 (2,3 x 1, 3 ) − ( x 2 , 3 )2

x3 − 3x 2

1,6 x 2 ,9 −2,3 x 1, 9 3x 2 − x 4,6

2 y +(3 y )

43

1

2y y y y

−1

+(3 y )

2

−1

[

−1

2

+ −1(3 y )

−1

2

+( −3 y )

−2

−1

2

+( −9 y )

−2

−2

](3)

(3)

44 (8 y ) 2 3 +(8 y ) −2 3

[

]

(8 y ) 3 (8) + −2 3 (8 y ) 3 (8) 3 16 (8 y ) −13 + −16 (8 y ) −5 3 3 3 −1

2

45

[

]

(16t ) 4 −(16t ) − 4 3 (16t ) −1 4 (16 ) − − 3 (16t ) −−7 4 (16 ) 4 4 3

48 46

−5

3

3

(16t ) −

1

4

27 t 2 −

27 t 27 t 18t 18t

47 dy

2

2

3

3

−1

3

−1

3

[

[

− −48

4

(15t ) −

7

4

4

]

1 3

27 t 2 2 1 −2 − = 27 t 3 −1 27 t 3   2   27 t 3 −27 t

−2

3

[ 3 (27t ) ](27 ) ] −[−18( 27 t ) −5

− −2

−5

3

3

1 x3 x 3 (0 ) −1(3 x 2 )  dy =3 x 2 +  dx ( x 3 )2     2   dy 0 −3 x =3 x 2 +  6 dx  x  dx

=x3 +

−3 x 2 dy =3 x 2 +  x6 dx 

48 du dx du dx du dx du dx

]

   

5 x x ( 0 ) −5(1)  = 2 x −7 +  x2   = x 2 −7 x +

0 −5  = 2 x −7 + 2   x   −5  = 2 x −7 + 2  x 

49 dy =u 3 −5u 2 + 7 2 du

dy =3u 2 du

3u 3u 2 ( 0 ) −7( 6u )  −10 u +  3u 4  

dy 0 −42 u  =3u 2 −10 u + 4  du  3u  dy  −42 u  =3u 2 −10 u +  4 du  3u 

50

(t 3 −5t 2 +7t −1) dx = dt t2 2 2 dx t (3t −10t +7 ) −(t 3 −5t 2 +7t −1)( 2t ) = dt (t 2 )2

(3t 4 −10t 3 +7t 2 ) −(2t 4 −10t 3 +14t 2 −2t ) dx = dt t4 4 3 2 dx 3t −10t +7t −2t 4 +10t 3 −14t 2 +2t = dt t4 dx 14 −7t 2 −2t = dt t4