Formulário M008 Capítulos 1 e 2

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FORMULÁRIO – M008 
PRINCIPAIS DIRETIVAS DE DERIVAÇÃO E INTEGRAÇÃO: 
 
[ ] 0=K
dx
d
 [ ] )(')( xfKxfK
dx
d ⋅=⋅ 
[ ] )(')()( 1 xfxfmxf
dx
d mm ⋅⋅= − 
[ ] )(')ln()()( xfaaa
dx
d xfxf ⋅⋅= 
( )[ ]
)()ln(
)('
)(log
xfa
xf
xf
dx
d
a ⋅
= 
( )[ ] ( ) )(')(cos)( xfxfxfsen
dx
d ⋅= 
( )[ ] ( ) )(')()(cos xfxfsenxf
dx
d ⋅−= 
( )[ ] ( ) )(')(sec)( 2 xfxfxftg
dx
d ⋅= 
( )[ ] ( ) )(')(seccos)(cot 2 xfxfxfg
dx
d ⋅−= 
[ ] )(')()()(')()( xgxfxgxfxgxf
dx
d ⋅+⋅=⋅ 
 
CKxdxK +=⋅ 
C
m
xf
dxxfxf
m
m +
+
=⋅⋅
+
 1
)(
)(')(
1
 
C
a
a
dxxfa
xf
xf +=⋅⋅ )ln(
)('
)(
)( 
( ) +=⋅ Cxfdxxf
xf
)(ln
)(
)('
 
( ) ( ) +−=⋅⋅ Cxfdxxfxfsen )(cos)(')( 
( ) ( ) +=⋅⋅ Cxfsendxxfxf )()(')(cos 
( ) ( )[ ] +=⋅⋅ Cxfdxxfxftg )(secln)(')( 
( ) ( ) +=⋅⋅ Cxftgdxxfxf )()(')(sec2 
( ) ( ) +−=⋅⋅ Cxfgdxxfxf )(cot)(')(seccos 2 
 +




=⋅
+
C
a
xf
arctg
a
dx
xfa
xf )(1
)(
)('
22
 
  ⋅−⋅=⋅ duvvudvu 
 
FÓRMULAS DE PROBABILIDADE: 
 
( ) ( )( )AP
BAP
ABP
∩≡| ( ) ( ) ( )( )AP
BPBAP
ABP
|
| = 
 
( ) ( )
dx
xdF
xf XX = ( ) [ ]xXPxFX ≤= 
 
[ ] ( )
=
=≤≤
b
ax
X xfbXaP 
[ ] ( )=≤≤
b
a
X dxxfbXaP . 
[ ] ( )
= =
=≤≤≤≤
d
cy
b
ax
XY yxfdYcbXaP ,, 
[ ] ( )
==
=≤≤≤≤
b
ax
XY
d
cy
dxdyyxfdYcbXaP ,, 
 
][][][][ BAPBPAPBAP ∩−+=∪ 
 
][][][ BPAPBAP ⋅=∩ se A e B forem 
independentes. 
 
 
[ ] ( ) ( )aFbFbXaP XX −=≤< 
 
 
( ) ( )
( )
( )ygx
X
Y
xg
xf
yf
1
'
−=
=