Profa Denise Maria Varella Martinez

Tarefa Unidade 2 - Gabarito

Utilizando a tabela de derivadas, obtenha a derivada de cada funo a seguir:

1) 4x3)x(fy +== 30dx

dx3

dx

)4(d

dx

)x3(d)x(f ' =+=+=

2) 3xxf(x) 2 = 3x2dx

)x(d3

dx

)x(d)x(f

2'

==

3) 3x12x2

7

3

xf(x) 2

3

++=

12x7x

122

)x2(7

3

x3

dx

3d

dx

dx12

dx

)x(d

2

7

dx

)x(d

3

1)x(f

2

223'

+=

=+=++=

4) 6x43

xf(x)

3

++= 4xdx

)6(d

dx

)x(d4

dx

)x(d

3

1)x(f 2

3' +=++=

5) x

1f(x) =

2

2111

'

x

1xx)1(

dx

)x(d)x(f ====

6) 2x

2f(x) =

3

3122

'

x

4x4x)2(2

dx

)x(d2)x(f ====

7) 2-x

1-xf(x) =

2222 )2x(

1

)2x(

1x2x

)2x(

)1)(1x()1)(2x(

)2x(

)'2x)(1x()'1x)(2x()x('f

=

+=

=

=

8) 3-x

xf(x) =

2222 )3x(

3

)3x(

x3x

)3x(

)1)(x()1)(3x(

)3x(

)'3x)(x()'x)(3x()x('f

=

=

=

=

9) )x3(ensf(x) = )x3cos(3dx

)x3(d)x3cos()x('f ==

10) )xcos(f(x) 2= )x(xsen2dx

)x(d)x(sen)x('f 2

22

==

11) )x3(ens.xf(x) =

)x3(sen)x3cos(x3

)1)(x3(sendx

)x3(d)x3(cos(x

dx

dx)x3(sen))x3(sen(

dx

d.x)x('f

+=

=+=+=

12) 1x2f(x) += 1x2

1

1x22

2)2()1x2(

2

1)1x2(

dx

d)1x2(

2

1)x('f 2

1

2

2

2

1

+=

+=+=++=

2

13)3 2 x3xf(x) +=

( )3 223/22

3

22

23

2223

3

3

12

)x3x(3

)3x2(

)x3x(3

)3x2(3x2)x3x(

3

1

xdx

d3)x(

dx

d)x3x(

3

1)x3x(

dx

d)x3x(

3

1)x('f

+

+=

+

+=++=

=

++=++=

14) xx eef(x) += xxxxxx

eedx

)x(dee

dx

)e(d

dx

)e(d)x('f

=

+=+=

15) 6)3xln(xf(x) 2 ++= ( )6x3x

3x2)6x3x

dx

d.

)6x3x(

1)x('f

dx

du

u

1

dx

)u(ln(d6x3xu

22

2

2

++

+=++

++=

=++=

16) 1)ln(xf(x) += ( )1x

1)1x

dx

d.

)1x(

1)x('f

+=+

+=

Determine a derivada indicada:

17) 1)ln(xf(x) += ?''y =

( )

2

211''

1

)1x(

1)1()1x(

dx

)1x(d)1x(1)x(f

)1x(1x

1)1x

dx

d.

)1x(

1)x('f

+=+=

++=

+=+

=++

=

18) 1x2f(x) += ?'''y =

2

1

2

1

2

2

2

1' )1x2(

1x2

1

1x22

2)2()1x2(

2

1)1x2(

dx

d)1x2(

2

1y)x('f

+=+

=

+=+=++==

( ) ( )2

3

33

2

3

2

2

2

1'''' )1x2(

1x2

1

1x22

2)2()1x2(

2

1)1x2(

dx

d)1x2(

2

1y)x(f

+=+

=

+=+=++==

( ) ( )552

5

2

2

2

3''''''

1x2

3

1x22

6)2()1x2(

2

3)1x2(

dx

d)1x2)(1(

2

3y)x(f

+=

+=+=++==

19) 3x12x2

7

3

xf(x) 2

3

++= ?y IV =

12x7x122

)x2(7

3

x3

dx

3d

dx

dx12

dx

)x(d

2

7

dx

)x(d

3

1)x(f 2

223' +=+=++=

7x2)x(f '' =

2)x(f ''' = 0)x(f IV =

3

Obtenha a equao da reta tangente ao grfico de f nos pontos indicados:

20) 33xf(x) = P(1,3)

2' x9y = o coeficiente angular da reta dado por 9)1(9)1(f 2' == ,

6x9y39x9y)1x(93y =+== .

21) xxf(x) 2 = P(2,2)

1x2y ' = o coeficiente angular da reta dado por 31)2(2)2(f ' == ,

4x3y26x3y)2x(32y =+== .