Regras de dieferenciação

Páginas: 2 (353 palavras) Publicado: 7 de abril de 2013
Regras de Diferenciação
d
1
arc sen ( x ) =
dx
1− x2
d
1
arc cos( x ) = −
dx
1− x2

1

d
(c ) = 0
dx

19

2

d
[c f (x )] = c f ' (x )
dx20

3

d
[f (x ) + g(x )] = f ' (x ) + g' (x )
dx

21

4

d
[f (x ) − g(x )] = f ' (x ) − g ' (x )
dx

22

5

d
[f (x ) g(x )] = f ' (x ) g(x )+ f (x ) g' (x )
dx

23

6

d  f (x )  f ' (x ) g(x ) − f (x ) g' (x )
=
dx  g(x ) 
[g(x )]2



24

d
1
arc cot g ( x ) = −
dx
1+ x2

7d
f (g ( x )) = f ' (g ( x )) g ' ( x )
dx

25

d
senh ( x ) = cosh( x )
dx

8

dn
( x ) = n x n −1
dx

26

d
cosh( x ) = senh ( x )
dx

9dx
(e ) = e x
dx

27

d
tgh ( x ) = sec h 2 ( x )
dx

10

dx
(a ) = a x ln(a )
dx

28

d
cos sec h ( x ) = − cos sec h ( x ) cot gh ( x )
dx11

d
1
ln x =
dx
x

29

d
sec h ( x ) = − sec h ( x ) tgh ( x )
dx

12

d
1
log a ( x ) =
dx
x ln(a )

30

d
cot gh ( x ) = − cos sec h 2( x )
dx

13

d
sen ( x ) = cos( x )
dx

31

14

d
cos( x ) = −sen ( x )
dx

32

15

d
tg ( x ) = sec 2 ( x )
dx

33

16

d
cos sec( x) = − cos sec( x ) cot( x )
dx

34

17

d
sec( x ) = sec( x ) tg ( x )
dx

35

d
1
arc sec h ( x ) = −
dx
x 1− x2

18

d
cot g ( x ) = − cossec2 ( x )
dx

36

d
1
arc cot gh ( x ) =
dx
1− x2

d
1
arc tg ( x ) =
dx
1+ x2
d
1
arc cos sec( x ) = −
dx
x x2 −1
d
1
arc sec( x ) =
dx
x x2 −1

d
1
arc senh ( x ) =
dx
1+ x2
d
1
arc cosh( x ) =
dx
x 2 −1
d
1
arc tgh ( x ) =
dx
1− x2
d
1
arc cos sec h ( x ) = −
dx
x x2 +1

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