Post on 24-Feb-2018
7/25/2019 Proyecto de Calculo Solusonario (1)
1/2
59. y=x21+x3; x=2
y=x2 (1+x3 )1
2
dy
dx
=x2 . d
dx
(1+x3 )1
2+(1+x3 )1/2 d
dx
(x2 )
dy
dx=x2
d
dx(1+x3 )
1
21 d
dx(1+x3)+ (1+x3 )1 /2(2x)
dy
dx=
x2 (1+x3 )1 /2 (3x2 )
2 +(1+x3 )
1/2(2x )
dydx=
3x
4
2 (1+x3 )1 /2+2x(1+x3 )
1/2
dy
dx=
3x4+(2x ) (2 )(1+x3 )1/2 (1+x3 )1 /2
2 (1+x3 )1/2
dy
dx=
3x4+4x (1+x3 )
2 (1+x3 )1 /2
dy
dx=
3x4+4x+4x4
2 (1+x3)1/ 2
dy
dx=
7x4+4x
2 (1+x3 )1/2
dy
dx=
7x4+4x
2 (1+x3 )1
/2
Reemplazamos x=2
dy
dx=
7 (2)4+4 (2)
2 (1+23 )1/2
dy
dx=
7 (16 )+8
29
dy
dx=
112+82(3)
7/25/2019 Proyecto de Calculo Solusonario (1)
2/2
dy
dx=
120
6
Respuesta:dy
dx=20
60. y=(4x2
)3
x=3
dy
dx=3(4x2 )31 d
dx(4x2 )
dy
dx=3 (4x2 )2 (2x )
dy
dx=6x
(4x2
)
2
Reemplazamos x=3
dy
dx=6(3) [4(3)2 ]
2
dy
dx=18( 49 )2
dy
dx=18 (5 )2
dy
dx=18(125 )
Respuesta:dy
dx=450