lista_derivadas_1

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CEFET-BA – DCA – COORDENAÇÃO DE MATEMÁTICA 
LISTA DE EXERCÍCIOS – DERIVADAS – Professor Caribé. 
 
Determine as derivadas das seguintes funções: 
1. )(.3 xseny = 
R: y´ = 3 cos(x) 
2. ).2cos(.3).3(.2 ttseny −= 
R: y´=6cos(3t) + 6sen(2t) 
3. )3).(2( +−= xxy 
R: y´= 2x + 1 4. 2.3
5.2
−
+
=
x
xy R: 2)23(
19
´
−
−
=
x
y 
5. 
2
1
1






−
+
=
x
xy R: 3)1(
)1(4
´
−
+−
=
x
xy 6. 3)(log xy = R: 3
2
))10(ln(
))(ln(3
´
x
xy = 
7. xxey )(= R: xexy 2´= 8. )( xexy = R: )1)(ln(´
x
xxey
xex += 
9. 
a
xy
35−
= R: 
a
xy
215
´
−
= 
10. nmm tbtay ++= .. 
R: 11 )(´ −+− ++= nmm tnmbamty 
11. )cos().cos( xarcxy = 
R: 
21
)cos()cos()(´
x
x
xarcxseny
−
−−= 
12. )(.)cos(
)cos(.)(
xsenxx
xxxseny
+
−
= 
R: 2
2
))()(cos(´ xxsenx
xy
+
= 
13. 






=
a
x
senarcy 
R: 
)(2
1
´
xax
y
−
= 
14. )ln()]([ xxseny = 
R: 




+= ))(ln(cot))(ln()(´ )ln( xg
x
xsen
xseny x 
15. 
22
6
.
ba
bxa
y
+
+
= R: 
22
56
´
ba
axy
+
= 
16. )1cosh( 2 +x 
R: 
)1cosh(
)1(
´
2
2
x
xsenhxy
+
+
= 
17. )](ln[ baxtgy += 
R: 
bax
baxay
+
+
=
)2sec(cos
´ 
18. ))(ln(cos xarcy = 
R: 
2))(ln(1
1
´
xx
y
−
−
= 
19. 21
..3
t
ta
x
+
= ; 2
2
1
..3
t
ta
y
+
= 
21
2
t
t
dx
dy
−
= 
20. ))(ln(cot.2 sgu = ; )(cot)( sgstgv += 
)2( stg
dv
du
= 
21. 222222 bayaxb =+ 
 
ya
xb
dx
dy
2
2
−= 
22. 0=−+ ayx 
 
x
y
dx
dy
−= 
 
23. 








++
+−
=
1
1
2
2
xx
xx
tgarcy 
R: 
)1)(1()1(2
)1(
´
222
2
+−+++
−
=
xxxxx
xy 
24. 33 2 xx
b
x
a
y −= 
R: 
3 53 7 3
2
3
4
´
x
a
x
by −= 
25. 
22
1
xa
y
−
= 
R: 
322 )(
´
xa
xy
−
= 
26. 
11
11
−++
−−+
=
xx
xxy 
R: 
)11(1
11
´
2
−++−
+−−
=
xxx
xxy 
27. 





−
+
=
2
2ln
x
xy p/ x > 2 
R: 
4
4
´ 2
−
−
=
x
y 
28. 22))(( xseny = 
 
R: )2(2´ 2xsenxy = 
29. ))2cos(1.(2
)(
x
xsen
y
+
= 
2
))(sec(
´
2xy = 
30. )2cos(1
)(
x
xsen
y
−
= 
0´=y