Taller No 8
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TALLER No.8 1)
x 5 =5x 4
2) x
3)
3
=x (3 )
1
=(3)
1
1 = t3 =
2
2
( x )( 2 )
1
(
t 3 (0 ) −1 3t 2
(t ) 3
2
2
)
0 −3t 2 t6 −3t 2 = t6 =
4)
4 = u4 u 4 (0 ) −4 4u 3 = 2 u4
(
)
0 −16 u = u8 −16 u 3 = u8 5)
(
3
1 = 5u 5 5u 5 (0 ) −1 25 u 4 = 2 5u 5
( )
(
)
)
0 −25 u 4 5u 10 −25 u 4 = 5u 10 =
6)
x7 = 7 7 7x6 =
(
=
) −x ( 0 )
(7 ) 2
49 x 6 −0 49
=
49 x 6 49
7
= 1
7) 3
x
2
49 x 6 49
=
1 x
=
= =
2
x
3
2
3
[
]
(0 ) −1 2 3 ( x ) −13 (1) 2
2 x 3
[
0 −1 2
x −2
3 x
(x)
3 4
− 1
3
]
3
( x ) −13 4
3
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) 4 x 3 +2 +1 x x (0 ) −1(1) =12 x 2 + x2 0 −1 =12 x 2 + 2 x −1 =12 x 2 + 2 x 13) 3u 2 + 3 2
u u 2 (0 ) −3( 2u ) =6u + 2 u2 0 −6u =6u + u4
(
)
−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 6 (x 6 )2 =
36 x 5 −0 0 −36 x 5 + 36 x 12
x6 6 + 6 6 x 6(6 x 5 ) −x 6 (0 ) x 6 (0 ) −6(6 x 5 ) = + 62 (x 6 )2 36 x 5 −0 0 −36 x 5 + 36 x 12 −36 x 5 36 x 5 −0 = + x 12 36 =
15) x 1, 2 + 1 x 0, 6 =1,2 x 0 , 2 +
x 0 , 6 (0 ) −1(0,6 x −0 , 4 )
(x ) 0,6
2
0 −0,6 x −0 , 4 =1,2 x 0 , 2 + x 1, 2 −0,6 x −0 , 4 =1,2 x 0 , 2 + x 1, 2
16) x 0 , 4 −x −0 , 4
=0,4 x −0 , 6 −(−0, 4 x −1, 4 )
17) 2
2
x +
=2 x
1
x 2 + 1 x 2
2
1 − 1 =2 x 2 +2 x 2
=2 x
1
2
+2 x
− 1
2
−1 + −x 2 1 7 7 18) x + 7 +7 x + +7 x x 7 x (0 ) −1 7 x 6 =7 x 6 + 2 x7
=x
− 1
2
(
)
0 −7 x 6 =7 x 6 + x 14
−7 x 6 =7 x 6 + x 14 19) 2
x3 +
(
) x (0 ) −7(1) +7 +
0 −7 +7 + x 2
−7 +7 + x 2
2 x3
3 2 =2 x 2 + 3 x 2 3 − 3 2 =2 x 2 +2 x
=2 x
3
=3 x
1
− 3
2
+2 x
2
− 5 2 +−3 x
2
x2
2
x3 +
2
x3
3 2 =2 x 2 + 3 x 2 3 − 3 2 =2 x 2 +2 x 3
=2 x
+2 x
2
− 3
2
− 5 2 + −3 x 20) 2 t − 3 3 t 1 3 =2 t 2 − 1 t 3 1
=3 x
2
=2 t =2t =t
21) 2 x
3
− 1
2
=3 x
22)
3
1
1
−3t
2
2
=x =x
1
3
3
=1
3
=1
3
5
3
4 1
+5 x
x −3 1
− 1
−4 3 − −t
2
+4 x 1
− 1 3 −3 t
2
4
1 x 1
−
1
x 3 − 1 −1 x 3 x x
−2
3
.−2
3
−1x
− 1
3
− −1 3 x
−4
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)
( x −7 )(2 x −9 ) =( x −7 )(2 ) +(2 x −9 )(1) =(2 x −14 ) +(2 x −9 ) 2
26) 1 x + x 1 x (0 ) −1(1) =2x + 1 + x x2 1 0 − 1 =2x + 1 + 2 x x
2
1 x + x
1 x (0 ) −1(1) =2x + 1 + x x2 1 0 −1 =2x + 1 + 2 x x 1 −1 =2x + 1 + 2 x x
27) (u +1)(2u +1)
=(u +1)(2 ) +(2u +1)(1) =(2u +2 ) +(2u +1) 2
28) 1 x + x
2
1 1 1 = x 2 + 1 x + x x 2
2
− 1 1 12 = x +1 x 2 x + x −1 1 1 2 =2 x + x 2 x + x 1 − 1 − 1 −3 =2 x 2 +1 x 2 1 2 x 2 + −1 2 x 2
29)
(t
+1)(3t −1)
2
=(t +1)2(3t −1)(3) +(3t −1) =(t +1)6(3t +1) +(3t −1)
(u −2 )3 2 =3(u −2 ) (1) 2 =3(u −2 )
31)
( x + 2) 3 2 = 3( x + 2 ) (1) 2 = 3( x + 2 )
32)
(1)
2
=(t +1)(18 t −6 ) +(3t −1)
30)
2
2
( x +1)( x −1) 2 2 =( x +1)2( x −1)(1) +( x −1) (1) 2 =( x +1)2( x −1) +( x −1) 2 =( x +1)( 2 x −2 ) +( x −1)
( x +1)( x −1) 2 2 =( x +1)2( x −1)(1) +( x −1) (1) 2 =( x +1)2( x −1) +( x −1) 2 =( x +1)( 2 x −2 ) +( x −1) 3
33) x +1 x
x +1 x (1) −( x +1)(1) =3 x2 x 2
x +1 x −( x +1) =3 x2 x 2
3
34) 2t −1 2t
2
2t −1 =3 2t
2 y (2 ) −(2t −1)( 2 ) (2t ) 2
2t −1 4t −(4t −2 ) =3 4x 2 2t 2
3
3
35) y +2 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 = =
37)
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
(x
+1) 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) = x2 2
2
(x
+1) 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) = x2 2
2 38) x −3 x +1 x 2 x −3 x +1 = 1 x 2
=
=
x
1
2
(2 x −3) −(x 2
[
(x) 2
− 1
(
(x)
− 1
2
−3 x +1) 1
2
]
(1)
2
1 x 2
x
1
2
(2 x −3) −(x 2
−3 x +1) 1
2
(1))
x 1 1 − 1 2 2 x 2 −3 x 2 −(x −3 x +1) 1 2 ( x ) 2 = x
(
)
39) t +3 t t
3 t + t = t
1
2
− 1 3 =t + t 2 t −3 t (0 ) −3(1) −1 2 =1 + t 2 2 t −3 0 −3 −1 2 =1 + t 2 2 t −3 −3 −1 2 =1 + 2 t 2 t
40)
( x +1) 2 =
+( x −1) x2 2 2 x 2 [2( x +1)(1) +2( x −1)(1)] −( x +1) +( x −1) (2 x ) 2
(x ) 2
2
x 2 [2( x +1) +2( x −1)] −( x +1) +( x −1) = x4 2
(2 x )
x 2 (2 x +2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) 2
=
2
4
2
( x +1) 2 =
+( x −1) x2 2 2 x 2 [2( x +1)(1) +2( x −1)(1)] −( x +1) +( x −1) (2 x ) 2
(x ) 2
2
x 2 [2( x +1) +2( x −1)] −( x +1) +( x −1) x4 2
=
2
(2 x )
x 2 (2 x +2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) = x4 2
(2 x = 41)
(2t
+2 x 2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) x4 2
3
+3)
2
1, 6
1,6 x 2 , 9 −2,3 x 2 , 9 =3 x 2 − x 4,6 −0,7 =3 x 2 − 4 , 6 x
2 y +(3 y ) =2 y =y =y =y
44)
2
+(2t −3) 4t 2 2 4t [2(2t +3)(2 ) −2(2t −3)(2 )] −(2t +3) −(2t −3) (4 ) = 4t 2 2 2 4t [4(2t +3) −2(2t −3)] −(2t +3) −(2t −3) (4 ) = 4t 2 2 2 4t (8t +12 ) −(8t −12 ) −(8t +3) −(2t −3) = 4t 2 2 2 ( 32t 2 +48t ) −(8t −12 ) −(8t +3) −(2t −3) = 4t 2 2
42) x 3 − x x 2,3 x 2 , 3 (1,6 x 0 , 6 ) −x 1, 6 (2,3 x 1, 3 ) =3 x 2 − (x 2,3 )2
43)
2
1
− 1 − 1 − 1
2
2 2 2
− 1
+(3 y )
− 1
[ ] ] +[−3(3 y ) + −1(3 y )
− 2
− 2
+( −9 y )
− 2
(8 y ) 2 3 +(8 y ) −2 3 −5 − 1 =2 (8 y ) 3 (8) + −2 (8 y ) 3 (8) 3 3 =16
− 1 ( 8 y) 3 3
[
[
+ −16
(8 y ) 3
−5
3
]
]
(8 y ) =2
2
+(8 y )
3
(8 y ) 3
=16
3
− 1
3
−2
3
[
(8) + −2 3 (8 y )
[
(8 y ) −13
+ −16
3
45) (16t ) 3 4 −(16t ) −3 4
=3
(16t ) 4
=48 46)
3
(16t ) 4
2
=27t
2
=27t
2
=18t
y 47) d d x
3
−
− 1
4
27t
2
3
−(27t )
− 1
3
[
[
− −48
(16t ) 4
−7
−2
d x
y 49) d d u
4
4
]
]
(16 )
−2
3
3
[ 3 (27t ) (27 )] ] −[−18(27t ) − −2
=
−5
−5
3
3
y =3x 2
1 x3 x3 +
y =3x 2
+
y =x3 +
y =3x 2
u 48) d
−7
3
−1(27t )
3
]
(16 ) − −3 4 (16t )
4
3
− 1
3
]
(8)
27t 2 1
3
=27t
−5
3
1
27t 2 −
=18t
− 1
(8 y )
−5
=
=
(0 )
−1(3 x 2
(x ) 3
)
2
0 −3 x 2 x6 −3 x 2 + x6
5 x x ( 0 ) −5(1) u = 2 x −7 + x2 0 −5 u = 2 x −7 + x2 −5 u = 2 x −7 + 2 x
u =x
2
−7 x +
7 +6 3u 2 3u 2 ( 0 ) −7( 6u ) y =3u 2 −1 0 u + 2 3u 2 0 −4 2 u y =3u 2 −1 0 u + 3u 4 2 u −4 y =3u 2 −10 u + 4 3u
y =u 3 −5u
2
+
(
)
d y d u
7 +6 3u 2 3u 2 ( 0 ) −7( 6u ) y =3u 2 −1 0 u + 2 3u 2 0 −4 2 u y =3u 2 −1 0 u + 3u 4 2 u −4 y =3u 2 −10 u + 4 3u
=
y =u 3 −5u
+
2
(
50) dx = dt
x =
(t
x = x = x = x = 51) y =
)
−5t 2 +7t −1 t2 3t 2 −10 t +7 − t 3 −5t 2 +7t −1 ( 2t )
3
t2
)
(
) ( (t ) +7t ) −(2t 2
(3t
4
−10 t 3
)
2
2
4
−10 t 3 +14 t 2 −2t
)
4
3t
4
−10 t
3
+7t
2
t −2t 4 +10 t 3 −14 t 2 +2t t4
t 4 −7t 2 +2t t4
x
dy 2 y =1 dx dy =2 x dx
(
)
1 − 1 =2 x 2 1 2 x 2 (1)
=2 x
1
2
1 x −1 2 2
1 − 1 = x 2 x 2 = x =1
52) u = 1 x 1 u = 1 x 2 − 1 u =1 x 2
u =x
− 1
2
du 2u −3 =1 dx −3
− 1 x 2 =1
−3
− 1 x 2 =1
−3
−4 −3 −3 − 1 − 1 2 2 2 − 1 x + x − 3 2 x −x 2 =1 2
−3
−1
− 1 2 x 2 − 1 2 x 2 − 1 2 x 2 − 1 2 x 2
x
−3
−4
2
−3 − 1 − 1 x 2 2 x 2 + −3 x 2
=1
u =x du 2u −3 =1 dx −3
− 1 x 2 =1
−3
− 1 x 2 =1
−3
−4 −3 −3 − 1 − 1 x 2 −3 2 x 2 −1 2 x 2 + −x 2 =1
−3
−3 −3 − 1 − 1 x 2 2 x 2 −1 2 x 2 + −3 x 2
− 1 2 x 2 − 1 2 x 2 − 1 2 x 2 − 1 2 x 2
−4
=1
t −3)
2
(4 )
2
(4 )
−1(3 x 2
)
)
2
−5(1) 2
−7( 6u ) 2
u
)
2
−7( 6u ) 2
)
2
u
)
t −1 ( 2t ) +14 t 2 −2t
)
−14 t 2 +2t
−3 −x 2 =1
− 1
−4
2
=1
−3 −x 2 =1
− 1
−4
2
=1
x 5 =5x 4
2) x
3)
3
=x (3 )
1
=(3)
1
1 = t3 =
2
2
( x )( 2 )
1
(
t 3 (0 ) −1 3t 2
(t ) 3
2
2
)
0 −3t 2 t6 −3t 2 = t6 =
4)
4 = u4 u 4 (0 ) −4 4u 3 = 2 u4
(
)
0 −16 u = u8 −16 u 3 = u8 5)
(
3
1 = 5u 5 5u 5 (0 ) −1 25 u 4 = 2 5u 5
( )
(
)
)
0 −25 u 4 5u 10 −25 u 4 = 5u 10 =
6)
x7 = 7 7 7x6 =
(
=
) −x ( 0 )
(7 ) 2
49 x 6 −0 49
=
49 x 6 49
7
= 1
7) 3
x
2
49 x 6 49
=
1 x
=
= =
2
x
3
2
3
[
]
(0 ) −1 2 3 ( x ) −13 (1) 2
2 x 3
[
0 −1 2
x −2
3 x
(x)
3 4
− 1
3
]
3
( x ) −13 4
3
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) 4 x 3 +2 +1 x x (0 ) −1(1) =12 x 2 + x2 0 −1 =12 x 2 + 2 x −1 =12 x 2 + 2 x 13) 3u 2 + 3 2
u u 2 (0 ) −3( 2u ) =6u + 2 u2 0 −6u =6u + u4
(
)
−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 6 (x 6 )2 =
36 x 5 −0 0 −36 x 5 + 36 x 12
x6 6 + 6 6 x 6(6 x 5 ) −x 6 (0 ) x 6 (0 ) −6(6 x 5 ) = + 62 (x 6 )2 36 x 5 −0 0 −36 x 5 + 36 x 12 −36 x 5 36 x 5 −0 = + x 12 36 =
15) x 1, 2 + 1 x 0, 6 =1,2 x 0 , 2 +
x 0 , 6 (0 ) −1(0,6 x −0 , 4 )
(x ) 0,6
2
0 −0,6 x −0 , 4 =1,2 x 0 , 2 + x 1, 2 −0,6 x −0 , 4 =1,2 x 0 , 2 + x 1, 2
16) x 0 , 4 −x −0 , 4
=0,4 x −0 , 6 −(−0, 4 x −1, 4 )
17) 2
2
x +
=2 x
1
x 2 + 1 x 2
2
1 − 1 =2 x 2 +2 x 2
=2 x
1
2
+2 x
− 1
2
−1 + −x 2 1 7 7 18) x + 7 +7 x + +7 x x 7 x (0 ) −1 7 x 6 =7 x 6 + 2 x7
=x
− 1
2
(
)
0 −7 x 6 =7 x 6 + x 14
−7 x 6 =7 x 6 + x 14 19) 2
x3 +
(
) x (0 ) −7(1) +7 +
0 −7 +7 + x 2
−7 +7 + x 2
2 x3
3 2 =2 x 2 + 3 x 2 3 − 3 2 =2 x 2 +2 x
=2 x
3
=3 x
1
− 3
2
+2 x
2
− 5 2 +−3 x
2
x2
2
x3 +
2
x3
3 2 =2 x 2 + 3 x 2 3 − 3 2 =2 x 2 +2 x 3
=2 x
+2 x
2
− 3
2
− 5 2 + −3 x 20) 2 t − 3 3 t 1 3 =2 t 2 − 1 t 3 1
=3 x
2
=2 t =2t =t
21) 2 x
3
− 1
2
=3 x
22)
3
1
1
−3t
2
2
=x =x
1
3
3
=1
3
=1
3
5
3
4 1
+5 x
x −3 1
− 1
−4 3 − −t
2
+4 x 1
− 1 3 −3 t
2
4
1 x 1
−
1
x 3 − 1 −1 x 3 x x
−2
3
.−2
3
−1x
− 1
3
− −1 3 x
−4
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)
( x −7 )(2 x −9 ) =( x −7 )(2 ) +(2 x −9 )(1) =(2 x −14 ) +(2 x −9 ) 2
26) 1 x + x 1 x (0 ) −1(1) =2x + 1 + x x2 1 0 − 1 =2x + 1 + 2 x x
2
1 x + x
1 x (0 ) −1(1) =2x + 1 + x x2 1 0 −1 =2x + 1 + 2 x x 1 −1 =2x + 1 + 2 x x
27) (u +1)(2u +1)
=(u +1)(2 ) +(2u +1)(1) =(2u +2 ) +(2u +1) 2
28) 1 x + x
2
1 1 1 = x 2 + 1 x + x x 2
2
− 1 1 12 = x +1 x 2 x + x −1 1 1 2 =2 x + x 2 x + x 1 − 1 − 1 −3 =2 x 2 +1 x 2 1 2 x 2 + −1 2 x 2
29)
(t
+1)(3t −1)
2
=(t +1)2(3t −1)(3) +(3t −1) =(t +1)6(3t +1) +(3t −1)
(u −2 )3 2 =3(u −2 ) (1) 2 =3(u −2 )
31)
( x + 2) 3 2 = 3( x + 2 ) (1) 2 = 3( x + 2 )
32)
(1)
2
=(t +1)(18 t −6 ) +(3t −1)
30)
2
2
( x +1)( x −1) 2 2 =( x +1)2( x −1)(1) +( x −1) (1) 2 =( x +1)2( x −1) +( x −1) 2 =( x +1)( 2 x −2 ) +( x −1)
( x +1)( x −1) 2 2 =( x +1)2( x −1)(1) +( x −1) (1) 2 =( x +1)2( x −1) +( x −1) 2 =( x +1)( 2 x −2 ) +( x −1) 3
33) x +1 x
x +1 x (1) −( x +1)(1) =3 x2 x 2
x +1 x −( x +1) =3 x2 x 2
3
34) 2t −1 2t
2
2t −1 =3 2t
2 y (2 ) −(2t −1)( 2 ) (2t ) 2
2t −1 4t −(4t −2 ) =3 4x 2 2t 2
3
3
35) y +2 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 = =
37)
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
(x
+1) 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) = x2 2
2
(x
+1) 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) = x2 2
2 38) x −3 x +1 x 2 x −3 x +1 = 1 x 2
=
=
x
1
2
(2 x −3) −(x 2
[
(x) 2
− 1
(
(x)
− 1
2
−3 x +1) 1
2
]
(1)
2
1 x 2
x
1
2
(2 x −3) −(x 2
−3 x +1) 1
2
(1))
x 1 1 − 1 2 2 x 2 −3 x 2 −(x −3 x +1) 1 2 ( x ) 2 = x
(
)
39) t +3 t t
3 t + t = t
1
2
− 1 3 =t + t 2 t −3 t (0 ) −3(1) −1 2 =1 + t 2 2 t −3 0 −3 −1 2 =1 + t 2 2 t −3 −3 −1 2 =1 + 2 t 2 t
40)
( x +1) 2 =
+( x −1) x2 2 2 x 2 [2( x +1)(1) +2( x −1)(1)] −( x +1) +( x −1) (2 x ) 2
(x ) 2
2
x 2 [2( x +1) +2( x −1)] −( x +1) +( x −1) = x4 2
(2 x )
x 2 (2 x +2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) 2
=
2
4
2
( x +1) 2 =
+( x −1) x2 2 2 x 2 [2( x +1)(1) +2( x −1)(1)] −( x +1) +( x −1) (2 x ) 2
(x ) 2
2
x 2 [2( x +1) +2( x −1)] −( x +1) +( x −1) x4 2
=
2
(2 x )
x 2 (2 x +2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) = x4 2
(2 x = 41)
(2t
+2 x 2 ) +(2 x −2 ) −(2 x 2 +2 x ) +( x −1) x4 2
3
+3)
2
1, 6
1,6 x 2 , 9 −2,3 x 2 , 9 =3 x 2 − x 4,6 −0,7 =3 x 2 − 4 , 6 x
2 y +(3 y ) =2 y =y =y =y
44)
2
+(2t −3) 4t 2 2 4t [2(2t +3)(2 ) −2(2t −3)(2 )] −(2t +3) −(2t −3) (4 ) = 4t 2 2 2 4t [4(2t +3) −2(2t −3)] −(2t +3) −(2t −3) (4 ) = 4t 2 2 2 4t (8t +12 ) −(8t −12 ) −(8t +3) −(2t −3) = 4t 2 2 2 ( 32t 2 +48t ) −(8t −12 ) −(8t +3) −(2t −3) = 4t 2 2
42) x 3 − x x 2,3 x 2 , 3 (1,6 x 0 , 6 ) −x 1, 6 (2,3 x 1, 3 ) =3 x 2 − (x 2,3 )2
43)
2
1
− 1 − 1 − 1
2
2 2 2
− 1
+(3 y )
− 1
[ ] ] +[−3(3 y ) + −1(3 y )
− 2
− 2
+( −9 y )
− 2
(8 y ) 2 3 +(8 y ) −2 3 −5 − 1 =2 (8 y ) 3 (8) + −2 (8 y ) 3 (8) 3 3 =16
− 1 ( 8 y) 3 3
[
[
+ −16
(8 y ) 3
−5
3
]
]
(8 y ) =2
2
+(8 y )
3
(8 y ) 3
=16
3
− 1
3
−2
3
[
(8) + −2 3 (8 y )
[
(8 y ) −13
+ −16
3
45) (16t ) 3 4 −(16t ) −3 4
=3
(16t ) 4
=48 46)
3
(16t ) 4
2
=27t
2
=27t
2
=18t
y 47) d d x
3
−
− 1
4
27t
2
3
−(27t )
− 1
3
[
[
− −48
(16t ) 4
−7
−2
d x
y 49) d d u
4
4
]
]
(16 )
−2
3
3
[ 3 (27t ) (27 )] ] −[−18(27t ) − −2
=
−5
−5
3
3
y =3x 2
1 x3 x3 +
y =3x 2
+
y =x3 +
y =3x 2
u 48) d
−7
3
−1(27t )
3
]
(16 ) − −3 4 (16t )
4
3
− 1
3
]
(8)
27t 2 1
3
=27t
−5
3
1
27t 2 −
=18t
− 1
(8 y )
−5
=
=
(0 )
−1(3 x 2
(x ) 3
)
2
0 −3 x 2 x6 −3 x 2 + x6
5 x x ( 0 ) −5(1) u = 2 x −7 + x2 0 −5 u = 2 x −7 + x2 −5 u = 2 x −7 + 2 x
u =x
2
−7 x +
7 +6 3u 2 3u 2 ( 0 ) −7( 6u ) y =3u 2 −1 0 u + 2 3u 2 0 −4 2 u y =3u 2 −1 0 u + 3u 4 2 u −4 y =3u 2 −10 u + 4 3u
y =u 3 −5u
2
+
(
)
d y d u
7 +6 3u 2 3u 2 ( 0 ) −7( 6u ) y =3u 2 −1 0 u + 2 3u 2 0 −4 2 u y =3u 2 −1 0 u + 3u 4 2 u −4 y =3u 2 −10 u + 4 3u
=
y =u 3 −5u
+
2
(
50) dx = dt
x =
(t
x = x = x = x = 51) y =
)
−5t 2 +7t −1 t2 3t 2 −10 t +7 − t 3 −5t 2 +7t −1 ( 2t )
3
t2
)
(
) ( (t ) +7t ) −(2t 2
(3t
4
−10 t 3
)
2
2
4
−10 t 3 +14 t 2 −2t
)
4
3t
4
−10 t
3
+7t
2
t −2t 4 +10 t 3 −14 t 2 +2t t4
t 4 −7t 2 +2t t4
x
dy 2 y =1 dx dy =2 x dx
(
)
1 − 1 =2 x 2 1 2 x 2 (1)
=2 x
1
2
1 x −1 2 2
1 − 1 = x 2 x 2 = x =1
52) u = 1 x 1 u = 1 x 2 − 1 u =1 x 2
u =x
− 1
2
du 2u −3 =1 dx −3
− 1 x 2 =1
−3
− 1 x 2 =1
−3
−4 −3 −3 − 1 − 1 2 2 2 − 1 x + x − 3 2 x −x 2 =1 2
−3
−1
− 1 2 x 2 − 1 2 x 2 − 1 2 x 2 − 1 2 x 2
x
−3
−4
2
−3 − 1 − 1 x 2 2 x 2 + −3 x 2
=1
u =x du 2u −3 =1 dx −3
− 1 x 2 =1
−3
− 1 x 2 =1
−3
−4 −3 −3 − 1 − 1 x 2 −3 2 x 2 −1 2 x 2 + −x 2 =1
−3
−3 −3 − 1 − 1 x 2 2 x 2 −1 2 x 2 + −3 x 2
− 1 2 x 2 − 1 2 x 2 − 1 2 x 2 − 1 2 x 2
−4
=1
t −3)
2
(4 )
2
(4 )
−1(3 x 2
)
)
2
−5(1) 2
−7( 6u ) 2
u
)
2
−7( 6u ) 2
)
2
u
)
t −1 ( 2t ) +14 t 2 −2t
)
−14 t 2 +2t
−3 −x 2 =1
− 1
−4
2
=1
−3 −x 2 =1
− 1
−4
2
=1
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