Secao 3-6 R

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SEÇÃO 3.6 DERIVADAS DE FUNÇÕES LOGARÍTMICAS  1
 1. 
1
( )
2
¢ = -f x x
 2. 2
2
( )
( 4)ln3
¢ = -
x
f x
x
 3. 
1
( )
( 1)ln10
¢ = - -f x x x
 4. 
1
( )
2
¢ =F x
x
 5. 2/3
1
( )
3 (ln )
¢ =G x
x x
 6. 
1
( ) ln
æ ö÷ç¢ = + ÷ç ÷çè ø
xF x e x
x
 7. 
3
( ) cotgh y y
y
¢ = +
 8. 2
1 ln
(1 )
+ -¢ = +
x x x
y
x x
 9. 
22(ln tg )sec
tg
¢ = x xy
x
 10. 3 2
( 1)
-¢ = -
x
y
x x
 11. 
1
( ln )
+¢ = +
x
y
x x x
 12. y ¢ = ln x + 1, y ¢¢ = 1/x
 13. y ¢ = 1/x, y ¢¢ = –1/x2
 14. 
2
2 2 2
2 2 2
, 
1 ( 1)
-¢ ¢¢= =+ +
x x
y y
x x
 15. ( )122( ) ; , 2 1¢ = - ¥+f x x
 16. ( )sen (ln )( ) , 0, ¢ = - ¥xf x
x
 17. 2
2
( ) ; 2
( 4)ln3
¢ = >-
x
f x x
x
 18. y = x + ln 2 – 1
 19. 4 2 3 2
12 48
(3 7) (8 1)
3 7 8 1
æ ö÷ç¢ = - - + ÷ç ÷çè ø- -
x
y x x
x x
 20. 
22/5 2 4
2
2 8
( 8) 2 1
5 8
+ æ ö÷ç¢ = + + + + ÷ç ÷÷çè ø+
x x xy x x e x
x x
 21. 
4 3
8
( 1) ( 5) 4 3 8
1 5 3( 3)
æ ö+ - ÷ç¢ = + - ÷ç ÷çè ø+ - --
x x
y
x x xx
 22. 
2
2
1 1
1 2( 1)1
é ù+¢ ê ú= -ê ú+ ++ë û
x x
y
x xx
 23. 
5 4
4 2 2 5 2
2 5 4 4
1
1( 1) ( 3) 2( 2) 3
é ù+ ê ú¢ = + - -ê ú++ + + +ë û
xe x x x
y
xx x x x
 24. 
3 4 2 2
1/3 3
( 1) sen 12 1
2cotg
31
x x x
y x
xx x
æ ö+ ÷ç ÷¢ ç= + - ÷ç ÷çè ø+
 25. y ¢ = 0
 26. y ¢ = (sen x)cos x (–sen x ln sen x + cos x cotg x)
 27. y ¢ = xxx [xx (ln x + 1) ln x + xx – 1]
3.6 RESPOSTAS