7/25/2019 Proyecto de Calculo Solusonario (1)

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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