Regras de dieferenciação

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 ) dx 20

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

7

d 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 9

dx
(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 ) dx 11

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 ) = − cos sec2 ( 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 x 2 −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