Taller No 7
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TALLER No. 7 1)
y =2 x 3 +4 x 2 −5 x +8 y =6 x 2 +8 x −5
2)
3 y =−5 +3 x − x 2 −7 x 3 2 6 y =3 − x −21x 2 2
3)
y = 2 x 2 +4 x −5
(
(
)
6
) (4 x +4 ) +4 x −5)
y =6 2 x 2 +4 x −5
(
5
y =24 x +24 2 x 2
4)
5
1 5 1 3 y = x 2 + x 2 5 3 3
1
5 1 2 3 1 + x x 2 5 2 3 3 5 3 1 y = x 2 + x 2 10 6 y =
5) y =(1 −x 2
6)
2 − 1
2
2
2
− 1
2
(−2 x )
2
6 4 3 + 2 − 3 x x x x (0 ) −6(1) x 2 (0 ) −4(2 x ) x 3 (0 ) −3(3 x 2 ) y = + − x2 (x 2 )2 (x 3 )2 y =
y =
7)
1
(1 −x ) =−x (1 −x )
y =1 y
)
2
−6 −8 x −9 x 2 + − x2 x4 x6
y =(x 3 −3 x )
4
y =4(x 3 −3 x ) (3 x 2 −3) 3
y =12 x 2 −12 (x 3 −3 x )
3
8)
(
y = x +x −1
)
2
( )[ ( )] y =2(x +x )(1 −x ) y =2 −2 x (x +x ) y =2 x +x −1 1 + −1x −2 −1
−2
9)
y =( x −1) y y y
−2
−1
( x +2 ) 4 3 3 4 2 =( x −1) 4( x +2 ) (1) +( x +2 ) 3( x +1) (1) 3 3 4 2 =( x −1) 4( x +2 ) +( x +2 ) 3( x +1) 3 3 4 2 =( x −1) (4 x +8) +( x +2 ) (3 x −3) 3
y =( x −1) y y y
( x +2 ) 4 3 3 4 2 =( x −1) 4( x +2 ) (1) +( x +2 ) 3( x +1) (1) 3 3 4 2 =( x −1) 4( x +2 ) +( x +2 ) 3( x +1) 3 3 4 2 =( x −1) (4 x +8) +( x +2 ) (3 x −3) 3
10) y =( x +2 ) 2 (2 −x )3
y =( x +2 ) 3(2 −x )
(−1) +(2 −x )3 2( x +2 )(1) 2 2 3 y =( x +2 ) −3(2 −x ) +(2 −x ) 2( x +2 ) 2 2 3 y =( x +2 ) (−6 +3 x ) +(2 −x ) 2 x +4 −3 2 y =( x +1) (x 2 +1) −4 −3 2 y =( x +1) −3(x 2 +1) (2 x ) +(x 2 +1) 2( x +1)(1) −4 −3 2 y =( x +2 ) −6 x ( x 2 +x ) +( x 2 +1) 2( x +1) −4 −3 2 y =( x +2 ) (−6 x 3 −6 x ) +(x 2 +1) 2 x +2 2
11)
12) y = y =
2
2 x +1 x 2 −1 x 2 −1(2 ) −2 x +1(2 x )
(x
2
−1)
2
2 x 2 −2 −4 x 2 +2 x x 4 +1 −2 x 2 −2 +2 x y = x 4 +1 y =
13) y =
y =
x x +1 x 2 +1(1) −x ( 2 x ) 2
(x
2
)
+1
2
x 2 +1 −2 x 2 x 4 +1 −x 2 +1 y = x 4 +1 y =
2
x +1 14) y = x −1
x −1(1) −x +1(1) x +1 y =2 ( x −1) 2 x −1 x +1 x −1 −x +1 y =2 x 2 +1 x −1 x +1 0 y =2 2 x − 1 x + 1 2 x +2 y = x −1
x +1 x −1 −x +1 y =2 x 2 +1 x −1 x +1 0 y =2 2 x −1 x +1 2 x +2 y = x −1
(
15) y = x 2 −x
(
)
−2
) (2 x −1) y =−4 x +2(x −x ) −3
y =−2 x 2 −x
−3
2
16) y = x 2 ( x +1) −1
y = x 2 −1( x +1)
−2
y = x 2 −1( x +1)
−2
y = x 2 (−x −1)
17) y =
y =
(x (x
(1) +( x +1) −1 (2 x )
(
−2
(
+ 2 x 2 +2 x
+ 2 x 2 +2 x
− 1
−1
1
2 2
) −9 ) (0 ) −11 ( x 2 1
−9
1
2 2
(
x 2 −9 − 1 2 0 −1 x x −9 2 y = x 2 −9 −1 2 −1 x x −9 2 y = 2 x −9
(
)
1
−9
2
) (2 x ) − 1
2
2
2
)
(
)
(
)
−x x 2 −9 y = x 2 −9 1 18) y = (16 −x 2 ) 12
−1
2
1 (16 −x ) (16 −x ) (0) −1 (−2 x ) 2 2
y =
)
)
1
2
2
(
)
16 −x 2 − 1 2 2 0 −1 −x 16 −x y = 16 −x 2
(
1
− 1
2
2
2
)
−1 2 −1 −x (16 −x ) 2 y = 16 −x 2
x (16 −x 2 ) y = 16 −x 2
− 1
19) y = y =
y =
2
x
( x +1) 1 2 ( x +1) 1 2 (1) −x (1 2 ( x +1) −12 (1))
[
[( x +1) ] ) −x ( 1 ( x +1) 2 1
( x +1) 1 2
2
2
− 1
x +1
2
]
y = y =
y = y =
x
( x +1) 1 2 ( x +1) 1 2 (1) −x (1 2 ( x +1) −12 (1))
[
[( x +1) ] ) −x ( 1 ( x +1) 2 1
( x +1)
1
( x +1)
1
20) y = (x
2
2
2
2
− 1
+2 ) x
1
2
− 1
2 x x (x +2 ) y =
− 1
x 2 (x 2 +2 )
y =(x 2 +2 )
− 1
y =
y =
y =
(x (x
(2 x ) −(x 2
2
1
2
(1)
x2
2
−(x 2 +2 ) 1 2
−(x 2 +2 )
2
1
2
x2
−(x 2 +2 )
2
+2 )
x2
− 1
21) y =
2
x +1 − 1 −x ( x +1) 2 2 x +1
x 1 (x 2 +2 ) 2 y =
y =
]
2
1
2
2x
5 5
) +10 ) (2 ) −2 x 1 (x 8 1 8
+10
1 8
(
x 5 +10
(2 x (2 x
5
+20
)
+10
5
2
2
(5 x )
8
)
−7
8
8
5
5
(x
2
8
(
1 8
3
−7
2
) (x +20 ) −10 x 8 (x +10)
22) y =( x +2 )
)
4 5 −2 x 5 x 8 x +10
1 8
(x
5
)
1
+10
5
5
+10
)
−7
8
8
)
+1
(
−1
) (2 x ) +(x +1) 3( x +2 ) (1) y =( x +2 ) −2 x (x +1) +(x +1) 3( x +2 ) y =( x +2 ) (−2 x −2 x ) +(x +1) (3 x +6 ) y =( x +2 ) −1 x 2 +1 3 3
2
3
3
−2
2
− 1
2
−2
2
− 1
2
10
9
x (2 x ) −x 2 +10(1) x2
9
2 x 2 −x 2 +10 x2
x 2 10 y =10 x
9
2
−2
x 2 +10 23) y = x x 2 10 y =10 x
− 1
2
x 2 10 x 2 +10 y =10 x x2
10
x 2 +10 y = x
9
x (2 x ) −x 2 +10(1) x2
9
2 x 2 −x 2 +10 x2
9
x 2 +10 x2
x 2 10 y =10 x x 2 10 y =10 x x 2 10 y =10 x
9
x 2 10 y =10 x (10 ) 9
x 2 10 y =100 x 24) y =
y =
(x (x
2
3 3
) −4 ) (0 ) −32 (x 3 2
−4
2
3 3
(
−4
3
)
) (3x ) − 1
3
2
x 3 −4 2 3 − 1 3 0 −3 2 x x −4 3 y = 4 3 3 x −4
(
)
( ) −6 x ( x −4 ) y = (x −4)
− 1
3
4
3
(
)
3
3
1
2 2 25) y = x +1 (2 x +4 ) 1 4
y =
(2 x +4 )
1
4
(
) (2 x ) −( x
1 x 2 +1 2
−1
2
[(2 x +4) ] 1
26) y =( x +2 ) −3 2 (3 x 2 +1) y =( x +2 )
−3
2
(6 x ) +(3 x 2
y =(6 x 2 +12 x )
−3
+(3 x 2
2
27) y = x 3 ( x 2 +3)−1
[ ( [−2 x(−x
y y
4
)
+1
3
+1) −3
3
6
3
−2
−2
4
2
4
4
[14 (2 x +4)
−5
− 1
2
−2
3
2
( x +2 ) 2 (1) 2 −5 +1) −3 ( x +2 ) 2 2
−2
2
1
2
) (2 x )] +(x +3) (3 x ) =x −3) ] +(3 x +9 x ) = x (−2 x −6 x ) +(3 x +9 x ) =(−2 x −6 x ) +(3 x +9 x )
y = x 3 −1 x 2 +3 y
2
2
2
− 1
− 1
2
− 1
−3
4
]
(2 )
(
y = x 3 x 2 +3
)
−1
[ ( [−2 x(−x
) (2 x )] +(x +3) (3 x ) =x −3) ] +(3 x +9 x ) = x (−2 x −6 x ) +(3 x +9 x ) =(−2 x −6 x ) +(3 x +9 x ) −2
y = x 3 −1 x 2 +3 y y y
3 3
6
4
3
y =6 x 5 +4 29) du = dy
x
1
4
1
2
2
2
− 1
− 1
− 1
2
+3 x
3
2
4
−2
+6 x
3
4
−2
3
28) y =x 6 +x
− 1
2
u =x 2 x =
du y = 2 dy ( y +1)
y
( y +1) 2 2
( y +1) 2 (1) −y[2( y +1)(1)] 2 ( y +1) 2 2 ( y +1) −y[2( y +1)] 4 ( ) y + 1 2 ( y +1) −2 y ( y +1) ( y +1) 4
du y =2 2 dy ( y +1)
[
du y =2 2 dy ( y +1) du y =2 2 dy ( y +1)
30) dy du
−2
2
3
− 1
2
=
y =
]
x x +2
x =u 3 −5 dy du dy du dy du
u 3 −5 u 3 −5 +2 u 3 −5 = 3 u −3 3 u −3 3u 2 −u 3 −5 3u 2 = 2 u 3 −3 =
(
dy du
=
dy du
=
3u
5
(
−9u
3
2
(u
−24 u 2
(u
)
−3
)
2
3
)
(
−3u 5 −15 u 2 −3
)
2
)
31) dv = dx
v = y −3 y = x 2 +2 x
(
)
−3 dv = x 2 +2 x dx −4 dv =−3 x 2 +2 x (2 x +2 ) dx −4 dv =−6 x −6 x 2 +2 x dx
(
)
(
32) d x = dv
)
x = y 3 +2 y −1 y =v
−1
2
−1 d x −1 2 3 =v +2 v 2 −1 dv −1 d x −1 2 =v +2v 2 −1 dv 2 −3 −3 − 1 dx =3 v 2 −1 2 v 2 + −v 2 dv
33) d y
= d x
y =v
−1
2
v = x 2 +5 dy dx dy dx dy dx dy dx
34) dx du
(
= x 2 +5 =−1
(x 2
)
− 1
2
+5
2
(
=−x x 2 +5
)
(
= −x 3 −5 x =
x =
)
−3
)
−3
2
(2 x )
2
−3
2
3 y −1 y +7
y =u 2 −5u
(
)
dx 3 u 2 −5u −1 = du u 2 −5u +7 dx 3u 2 −15u −1 = 2 du u −5u +7 dx u 2 −5u +7 (6u −15) − 3u 2 −15u −1 (2u −5) = 2 du u 2 −5u +7
( (
dx 6u = du
)
3
−15u
2
(
(
−30u
2
)
)
) (
+75u +42u −105 − 6u 3 −15u 2 −30u 2 +75u −2u +5
(u
2
−5u +7
)
2
)
dx = du
x =
3 y −1 y +7
y =u 2 −5u
(
)
dx 3 u 2 −5u −1 = du u 2 −5u +7 dx 3u 2 −15u −1 = 2 du u −5u +7 dx u 2 −5u +7 (6u −15) − 3u 2 −15u −1 (2u −5) = 2 du u 2 −5u +7
( (
)
dx 6u = du
3
−15u
2
(
−30u
dx 6u −15u −30u = du dx −44u −110 = 4 du u −25u 2 +49 3
2
(
2
2
)
)
) (
+75u +42u −105 − 6u 3 −15u 2 −30u 2 +75u −2u +5
(u
2
−5u +7
)
2
+75u +42u −105 −6u +15u 2 +30u 2 −75u +2u −5 u 4 −25u 2 +49 3
)
(2 x +4 )
−3
4
]
(2 )
−30u 2 +75u −2u +5
)
−30u 2 +75u −2u +5
+30u 2 −75u +2u −5
)
y =2 x 3 +4 x 2 −5 x +8 y =6 x 2 +8 x −5
2)
3 y =−5 +3 x − x 2 −7 x 3 2 6 y =3 − x −21x 2 2
3)
y = 2 x 2 +4 x −5
(
(
)
6
) (4 x +4 ) +4 x −5)
y =6 2 x 2 +4 x −5
(
5
y =24 x +24 2 x 2
4)
5
1 5 1 3 y = x 2 + x 2 5 3 3
1
5 1 2 3 1 + x x 2 5 2 3 3 5 3 1 y = x 2 + x 2 10 6 y =
5) y =(1 −x 2
6)
2 − 1
2
2
2
− 1
2
(−2 x )
2
6 4 3 + 2 − 3 x x x x (0 ) −6(1) x 2 (0 ) −4(2 x ) x 3 (0 ) −3(3 x 2 ) y = + − x2 (x 2 )2 (x 3 )2 y =
y =
7)
1
(1 −x ) =−x (1 −x )
y =1 y
)
2
−6 −8 x −9 x 2 + − x2 x4 x6
y =(x 3 −3 x )
4
y =4(x 3 −3 x ) (3 x 2 −3) 3
y =12 x 2 −12 (x 3 −3 x )
3
8)
(
y = x +x −1
)
2
( )[ ( )] y =2(x +x )(1 −x ) y =2 −2 x (x +x ) y =2 x +x −1 1 + −1x −2 −1
−2
9)
y =( x −1) y y y
−2
−1
( x +2 ) 4 3 3 4 2 =( x −1) 4( x +2 ) (1) +( x +2 ) 3( x +1) (1) 3 3 4 2 =( x −1) 4( x +2 ) +( x +2 ) 3( x +1) 3 3 4 2 =( x −1) (4 x +8) +( x +2 ) (3 x −3) 3
y =( x −1) y y y
( x +2 ) 4 3 3 4 2 =( x −1) 4( x +2 ) (1) +( x +2 ) 3( x +1) (1) 3 3 4 2 =( x −1) 4( x +2 ) +( x +2 ) 3( x +1) 3 3 4 2 =( x −1) (4 x +8) +( x +2 ) (3 x −3) 3
10) y =( x +2 ) 2 (2 −x )3
y =( x +2 ) 3(2 −x )
(−1) +(2 −x )3 2( x +2 )(1) 2 2 3 y =( x +2 ) −3(2 −x ) +(2 −x ) 2( x +2 ) 2 2 3 y =( x +2 ) (−6 +3 x ) +(2 −x ) 2 x +4 −3 2 y =( x +1) (x 2 +1) −4 −3 2 y =( x +1) −3(x 2 +1) (2 x ) +(x 2 +1) 2( x +1)(1) −4 −3 2 y =( x +2 ) −6 x ( x 2 +x ) +( x 2 +1) 2( x +1) −4 −3 2 y =( x +2 ) (−6 x 3 −6 x ) +(x 2 +1) 2 x +2 2
11)
12) y = y =
2
2 x +1 x 2 −1 x 2 −1(2 ) −2 x +1(2 x )
(x
2
−1)
2
2 x 2 −2 −4 x 2 +2 x x 4 +1 −2 x 2 −2 +2 x y = x 4 +1 y =
13) y =
y =
x x +1 x 2 +1(1) −x ( 2 x ) 2
(x
2
)
+1
2
x 2 +1 −2 x 2 x 4 +1 −x 2 +1 y = x 4 +1 y =
2
x +1 14) y = x −1
x −1(1) −x +1(1) x +1 y =2 ( x −1) 2 x −1 x +1 x −1 −x +1 y =2 x 2 +1 x −1 x +1 0 y =2 2 x − 1 x + 1 2 x +2 y = x −1
x +1 x −1 −x +1 y =2 x 2 +1 x −1 x +1 0 y =2 2 x −1 x +1 2 x +2 y = x −1
(
15) y = x 2 −x
(
)
−2
) (2 x −1) y =−4 x +2(x −x ) −3
y =−2 x 2 −x
−3
2
16) y = x 2 ( x +1) −1
y = x 2 −1( x +1)
−2
y = x 2 −1( x +1)
−2
y = x 2 (−x −1)
17) y =
y =
(x (x
(1) +( x +1) −1 (2 x )
(
−2
(
+ 2 x 2 +2 x
+ 2 x 2 +2 x
− 1
−1
1
2 2
) −9 ) (0 ) −11 ( x 2 1
−9
1
2 2
(
x 2 −9 − 1 2 0 −1 x x −9 2 y = x 2 −9 −1 2 −1 x x −9 2 y = 2 x −9
(
)
1
−9
2
) (2 x ) − 1
2
2
2
)
(
)
(
)
−x x 2 −9 y = x 2 −9 1 18) y = (16 −x 2 ) 12
−1
2
1 (16 −x ) (16 −x ) (0) −1 (−2 x ) 2 2
y =
)
)
1
2
2
(
)
16 −x 2 − 1 2 2 0 −1 −x 16 −x y = 16 −x 2
(
1
− 1
2
2
2
)
−1 2 −1 −x (16 −x ) 2 y = 16 −x 2
x (16 −x 2 ) y = 16 −x 2
− 1
19) y = y =
y =
2
x
( x +1) 1 2 ( x +1) 1 2 (1) −x (1 2 ( x +1) −12 (1))
[
[( x +1) ] ) −x ( 1 ( x +1) 2 1
( x +1) 1 2
2
2
− 1
x +1
2
]
y = y =
y = y =
x
( x +1) 1 2 ( x +1) 1 2 (1) −x (1 2 ( x +1) −12 (1))
[
[( x +1) ] ) −x ( 1 ( x +1) 2 1
( x +1)
1
( x +1)
1
20) y = (x
2
2
2
2
− 1
+2 ) x
1
2
− 1
2 x x (x +2 ) y =
− 1
x 2 (x 2 +2 )
y =(x 2 +2 )
− 1
y =
y =
y =
(x (x
(2 x ) −(x 2
2
1
2
(1)
x2
2
−(x 2 +2 ) 1 2
−(x 2 +2 )
2
1
2
x2
−(x 2 +2 )
2
+2 )
x2
− 1
21) y =
2
x +1 − 1 −x ( x +1) 2 2 x +1
x 1 (x 2 +2 ) 2 y =
y =
]
2
1
2
2x
5 5
) +10 ) (2 ) −2 x 1 (x 8 1 8
+10
1 8
(
x 5 +10
(2 x (2 x
5
+20
)
+10
5
2
2
(5 x )
8
)
−7
8
8
5
5
(x
2
8
(
1 8
3
−7
2
) (x +20 ) −10 x 8 (x +10)
22) y =( x +2 )
)
4 5 −2 x 5 x 8 x +10
1 8
(x
5
)
1
+10
5
5
+10
)
−7
8
8
)
+1
(
−1
) (2 x ) +(x +1) 3( x +2 ) (1) y =( x +2 ) −2 x (x +1) +(x +1) 3( x +2 ) y =( x +2 ) (−2 x −2 x ) +(x +1) (3 x +6 ) y =( x +2 ) −1 x 2 +1 3 3
2
3
3
−2
2
− 1
2
−2
2
− 1
2
10
9
x (2 x ) −x 2 +10(1) x2
9
2 x 2 −x 2 +10 x2
x 2 10 y =10 x
9
2
−2
x 2 +10 23) y = x x 2 10 y =10 x
− 1
2
x 2 10 x 2 +10 y =10 x x2
10
x 2 +10 y = x
9
x (2 x ) −x 2 +10(1) x2
9
2 x 2 −x 2 +10 x2
9
x 2 +10 x2
x 2 10 y =10 x x 2 10 y =10 x x 2 10 y =10 x
9
x 2 10 y =10 x (10 ) 9
x 2 10 y =100 x 24) y =
y =
(x (x
2
3 3
) −4 ) (0 ) −32 (x 3 2
−4
2
3 3
(
−4
3
)
) (3x ) − 1
3
2
x 3 −4 2 3 − 1 3 0 −3 2 x x −4 3 y = 4 3 3 x −4
(
)
( ) −6 x ( x −4 ) y = (x −4)
− 1
3
4
3
(
)
3
3
1
2 2 25) y = x +1 (2 x +4 ) 1 4
y =
(2 x +4 )
1
4
(
) (2 x ) −( x
1 x 2 +1 2
−1
2
[(2 x +4) ] 1
26) y =( x +2 ) −3 2 (3 x 2 +1) y =( x +2 )
−3
2
(6 x ) +(3 x 2
y =(6 x 2 +12 x )
−3
+(3 x 2
2
27) y = x 3 ( x 2 +3)−1
[ ( [−2 x(−x
y y
4
)
+1
3
+1) −3
3
6
3
−2
−2
4
2
4
4
[14 (2 x +4)
−5
− 1
2
−2
3
2
( x +2 ) 2 (1) 2 −5 +1) −3 ( x +2 ) 2 2
−2
2
1
2
) (2 x )] +(x +3) (3 x ) =x −3) ] +(3 x +9 x ) = x (−2 x −6 x ) +(3 x +9 x ) =(−2 x −6 x ) +(3 x +9 x )
y = x 3 −1 x 2 +3 y
2
2
2
− 1
− 1
2
− 1
−3
4
]
(2 )
(
y = x 3 x 2 +3
)
−1
[ ( [−2 x(−x
) (2 x )] +(x +3) (3 x ) =x −3) ] +(3 x +9 x ) = x (−2 x −6 x ) +(3 x +9 x ) =(−2 x −6 x ) +(3 x +9 x ) −2
y = x 3 −1 x 2 +3 y y y
3 3
6
4
3
y =6 x 5 +4 29) du = dy
x
1
4
1
2
2
2
− 1
− 1
− 1
2
+3 x
3
2
4
−2
+6 x
3
4
−2
3
28) y =x 6 +x
− 1
2
u =x 2 x =
du y = 2 dy ( y +1)
y
( y +1) 2 2
( y +1) 2 (1) −y[2( y +1)(1)] 2 ( y +1) 2 2 ( y +1) −y[2( y +1)] 4 ( ) y + 1 2 ( y +1) −2 y ( y +1) ( y +1) 4
du y =2 2 dy ( y +1)
[
du y =2 2 dy ( y +1) du y =2 2 dy ( y +1)
30) dy du
−2
2
3
− 1
2
=
y =
]
x x +2
x =u 3 −5 dy du dy du dy du
u 3 −5 u 3 −5 +2 u 3 −5 = 3 u −3 3 u −3 3u 2 −u 3 −5 3u 2 = 2 u 3 −3 =
(
dy du
=
dy du
=
3u
5
(
−9u
3
2
(u
−24 u 2
(u
)
−3
)
2
3
)
(
−3u 5 −15 u 2 −3
)
2
)
31) dv = dx
v = y −3 y = x 2 +2 x
(
)
−3 dv = x 2 +2 x dx −4 dv =−3 x 2 +2 x (2 x +2 ) dx −4 dv =−6 x −6 x 2 +2 x dx
(
)
(
32) d x = dv
)
x = y 3 +2 y −1 y =v
−1
2
−1 d x −1 2 3 =v +2 v 2 −1 dv −1 d x −1 2 =v +2v 2 −1 dv 2 −3 −3 − 1 dx =3 v 2 −1 2 v 2 + −v 2 dv
33) d y
= d x
y =v
−1
2
v = x 2 +5 dy dx dy dx dy dx dy dx
34) dx du
(
= x 2 +5 =−1
(x 2
)
− 1
2
+5
2
(
=−x x 2 +5
)
(
= −x 3 −5 x =
x =
)
−3
)
−3
2
(2 x )
2
−3
2
3 y −1 y +7
y =u 2 −5u
(
)
dx 3 u 2 −5u −1 = du u 2 −5u +7 dx 3u 2 −15u −1 = 2 du u −5u +7 dx u 2 −5u +7 (6u −15) − 3u 2 −15u −1 (2u −5) = 2 du u 2 −5u +7
( (
dx 6u = du
)
3
−15u
2
(
(
−30u
2
)
)
) (
+75u +42u −105 − 6u 3 −15u 2 −30u 2 +75u −2u +5
(u
2
−5u +7
)
2
)
dx = du
x =
3 y −1 y +7
y =u 2 −5u
(
)
dx 3 u 2 −5u −1 = du u 2 −5u +7 dx 3u 2 −15u −1 = 2 du u −5u +7 dx u 2 −5u +7 (6u −15) − 3u 2 −15u −1 (2u −5) = 2 du u 2 −5u +7
( (
)
dx 6u = du
3
−15u
2
(
−30u
dx 6u −15u −30u = du dx −44u −110 = 4 du u −25u 2 +49 3
2
(
2
2
)
)
) (
+75u +42u −105 − 6u 3 −15u 2 −30u 2 +75u −2u +5
(u
2
−5u +7
)
2
+75u +42u −105 −6u +15u 2 +30u 2 −75u +2u −5 u 4 −25u 2 +49 3
)
(2 x +4 )
−3
4
]
(2 )
−30u 2 +75u −2u +5
)
−30u 2 +75u −2u +5
+30u 2 −75u +2u −5
)
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