Tabela de derivadas

Regras de Diferenciação d (c ) = 0 dx

1

19

2

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

20

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

3

21

4

22

5

23

6

d  f (x )  f ' (x ) g(x ) − f (x ) g' (x ) = dx  g(x )  [g(x )]2   d f (g ( x )) = f ' (g ( x )) g ' ( x ) dx d n ( x ) = n x n −1 dx d x (e ) = e x dx d x (a ) = a x ln(a ) dx d 1 ln x = dx x

24

7

25

8

26

9

27

10

28

11

29

12

d 1 log a ( x ) = dx x ln(a ) d sen ( x ) = cos( x ) dx d cos( x ) = −sen ( x ) dx d tg ( x ) = sec 2 ( x ) dx d cos sec( x ) = − cos sec( x ) cot( x ) dx d sec( x ) = sec( x ) tg ( x ) dx d cot g ( x ) = − cos sec2 ( x ) dx

30

d cot gh ( x ) = − cos sec h 2 ( x ) dx 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 d 1 arc sec h ( x ) = − dx x 1− x2 d 1 arc cot gh ( x ) = dx 1− x2

13

31

14

32

15

33

16

34

17

35

18

36