Material de apoio – Exercícios - Derivadas
a )Dadas as funções deriváveis abaixo, determine as suas respectivas derivadas:
( )
5
=
xf
( )
xxf 3
=
( )
3
x
xf
=
( )
2
xxf
=
( )
6
xxf
=
( )
x
xf 1
=
( )
3
1
x
xf
=
( )
xxf
=
( )
100
xxf
=
( )
3
−
=
xxf
( )
xxg 12
=
( )
xxg 5
−=
( )
x
xg 9
−=
( )
2
2
3xxg
=
( )
53
=
xg
( )
0
8xxg
=
( )
xxg 9
=
( )
13
−
=
xxg
( )
2
4xxg
=
( )
5
5
1
−
=
xxg
b) Dadas as funções deriváveis abaixo, determine as suas respectivas derivadas:
( )
x
xg 3
=
( )
x
xg 4
=
( )
x
xg 100
=
( )
x
.xg 10
10
1
=
( )
x
exg
=
( )
11
8xxf
=
( )
7
3
3
7
3
−−=
xxf
( )
2
35 xxxf
++=
( )
52
53 xxxf
++=
( )
5
23
+++=
xxxxf
( )
n
xxf 23
+=
( )
xsenxxf
+=
2
4
( ) ( )
3
1
−=
xxf
( )
xcosxsenxxf
−+−=
( )
4
xaxxf
−=
( )
x
xxf 38
4
−=
( )
x
excosxf
−=
( )
x
xxx
xf
x
45
4
−−
=
( )
xxxf 95
4
−=
( )
xsenexf
xx
++=
5
( )
2
3
+=
xxf
( )
32
1
++=
xxxf
( )
( )
xxxf
+=
2
cos
( )
( )
2
sen xxf
=
( )
)ln(sen xxf
=
( )
( )
3
2
13
+=
xxf
( ) ( )
xxf 3cos
=
( )
( )
3ln
2
+=
xxf
( )
x
exf
3
=
( )
x
exf
sen
=
( ) ( )
xxg cossen
=
( )
( )
x
exg cos
=
( )
x
exg
5
−
=
( )
( )
4
2
3
+=
ttg
( ) ( )
xxg 3sec
=
( )
( )
2
cot xgxg
=
( ) ( )
xxg 2seccos
=
( ) ( )
tgxxg sec
=
( )
xx
eexg
−
+=
c)Dadas as funções deriváveis abaixo, determine as suas respectivas derivadas:
( )
( )( )
32
13 xxxxxg
+++=
( )
( )( )
342
1xxxxxxg
+++=
( )
x
exxg
3
=
( )
xcosxexg
x
+=
( )
x
axxg
4
=
( ) ( )
ℜ∈+=
b,axcosbxsenaxg
( )
xcos.e.xxg
x
=
( )
x
exxg 2
2
+=
( )
xcos.xsen.exg
x
=
( )
x
exxg
2
54
+=
( )
7
2
x
xf
=
( )
1
1
2
++
=
xx
xf
( )
1
1
−
+
=
x
x
xf
