Upload
ricardo-gomes
View
212
Download
0
Embed Size (px)
DESCRIPTION
derivada
Citation preview
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 =+== .