My arquivo FORMULÁRIO CÁLCULO I

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Universidade Luterana do Brasil

DISCIPLINA: CÁLCULO I – FORMULÁRIO Nº 1 3 5 7 9

11

FUNÇÕES E DERIVADAS



y  k  y' 0

2 n 1

y  x  y1  n . x y   f ( x)  g ( x)  y '  f ' ( x)  g ' ( x) n

y  a x  y'  a x . ln a 1 y  log a x  y '  x. ln a y  u.v 

y '  u .v '  v . u '

4 6

15 17

y  sen x  y '  cos x

y  tan x  y'  sec x y  sec x  y '  sec x . tan x 2

y  x  y'  1 y  k . f ( x)  y '  k . f ' ( x)

FUNÇÃO RAIZ – TRANSFORMAR EM POTÊNCIA

8

y  e x  y'  e x

10

y  ln x  y '  u  v

1 x v . u '  u .v ' y'  v2

12

y

14

y  cos x  y '   sen x

FUNÇÕES TRIGONOMÉTRICAS 13

FUNÇÕES E DERIVADAS

16 18

y  cot x  y '   csc 2 x y  csc x  y '  csc x . cot x

REGRA DA CADEIA 19

y  f ( g ( x))  y '  f ' ( g ( x)).g ' ( x)

20

y  u n  y '  n . u n1 .u '

25

y  a u  y '  a u . ln a.u ' , a  0, a  1 u' u' y  log a u  y '  log a e ou y '  u u. ln a y  sen u  y ' u '.cos u

27

y  tan u  y '  u . sec 2 u

28

29

y  sec u  y'  u ' . sec u . tan u

30

y  cot u  y'   u '. csc 2 u y  csc u  y '   u '.csc u . cot u

32

y  arc cos u  cos 1 u  y ' 

34

y  arc cot u  y ' 

21 23

22 24 26

y  eu  y '  eu .u ' u' 1 y  ln u  y '  .u '  u u y  cos u  y '   u '. sen u

FUNCOES TRIGONOMÉTRICAS INVERSAS 31

33

35

y  arc sen u  sen 1u  y ' 

u'

1 u2 u' y  arc tan u  tan 1 x  y '  1 u2 u' , u 1 y  arc sen u, u  1  y '  u . u2 1

 u' 1 u2

36

y  arc csc u, u  1  y ' 

3

csc 2 x  1  cotg 2 x

 u' 1 u2

 u'

u . u2 1

, u 1

IDENTIDADES TRIGONOMÉTRICAS 1 5 9 11

sec 2 x  1  tg 2 x 1 cos x cot x   6 tan x sen x 1  cos 2 x sen 2 x  2 2sen x. cos y  sen ( x  y )  sen ( x  y )

sen 2 x  cos 2 x  1 sen x tan x  cos x

2

7 10 12

13

2 cos x . cos y  cos ( x  y)  cos ( x  y)

14

15

sen ( x)   sen x

16

17

tan ( x)   tan x

18

19

sen x x 1  cos x tan ( )   2 sen x 1  cos x

20

sec x 

1 cos x

4 8

sen 2 x  2 . sen x . cos x

csc x 

1 sen x

1  cos 2 x 2 2 sen x . sen y  cos(x  y)  cos(x  y)  1  sen x  1  cos (  x) 2 cos ( x)  cos x 2 tan x tan (2 x)  1  tan 2 x cos 2 x 

tan ( x  y ) 

tan x  tan y 1  tan x. tan y
My arquivo FORMULÁRIO CÁLCULO I

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