TABELA: Derivadas, Integrais e Identidades Trigonométricas
• Derivadas
1)
[
]
[
]
)(')(')(
1
xfxfnyxfy
nn
⋅⋅=⇒=
−
2) )(')()()('')()( xgxfxgxfyxgxfy ⋅+⋅=⇒⋅=
3)
[ ]
2
)(
)(')()()('
'
)(
)(
xg
xgxfxgxf
y
xg
xf
y⋅−⋅
=⇒=
4) )(')ln('
)()(
xfaayay
xfxf
⋅⋅=⇒=
5)
[ ]
)('
)ln()(
1
')(log xf
axf
yxfy
a
⋅
⋅
=⇒=
6)
[
]
[
]
)(')(cos')(sen xfxfyxfy ⋅=⇒=
7)
[
]
[
]
)(')(sen')(cos xfxfyxfy ⋅−=⇒=
8)
[
]
[
]
)(')(sec')(tg
2
xfxfyxfy ⋅=⇒=
9)
[
]
[
]
)(')(cossec')(cotg
2
xfxfyxfy ⋅−=⇒=
10)
[
]
[
]
[
]
)(')(t)(sec')(sec xfxfgxfyxfy ⋅⋅=⇒=
11)
[
]
[
]
[
]
)(')(cotg)(cossec')(cossec xfxfxfyxfy ⋅⋅−=⇒=
12)
[ ] [ ]
)('
)(1
1
')(arcsen
2
xf
xf
yxfy ⋅
−
=⇒=
13)
[ ] [ ]
)('
)(1
1
')(arccos
2
xf
xf
yxfy ⋅
−
−
=⇒=
14)
[ ] [ ]
)('
)(1
1
')(arctg
2
xf
xf
yxfy ⋅
+
=⇒=
15)
[ ] [ ]
)('
)(1
1
')(arccotg
2
xf
xf
yxfy ⋅
+
−
=⇒=
16)
[ ] [ ]
)('
1)()(
1
')(arcsec
,1)( Para
2
xf
xfxf
yxfy
xf
⋅
−⋅
=⇒=
>
17)
[ ] [ ]
)('
1)()(
1
')(arccossec
,1)( Para
2
xf
xfxf
yxfy
xf
⋅
−⋅
−
=⇒=
>
• Integrais
1)
[ ]
[
]
C
n
xf
dxxfxf
n
n
+
+
=⋅⋅
+
∫
1
)(
)(')(
1
2)
[ ]
∫
+=⋅ Cxfdx
xf
xf )(ln
)(
)('
3) C
a
a
dxxfa
xf
xf
+=⋅⋅
∫
)ln(
)('
)(
)(
4)
[ ] [ ]
Cxfdxxfxf +−=⋅⋅
∫
)(cos)(')(sen
5)
[ ] [ ]
Cxfdxxfxf +=⋅⋅
∫
)(sen)(')(cos
6)
[ ]
( )
[ ]
Cxfdxxfxf +−=⋅⋅
∫
)(cosln)(')(t g
7)
[ ]
( )
[ ]
Cxfdxxfxf +=⋅⋅
∫
)(senln)(')(cotg
8)
[ ]
( ) ( )
[ ]
Cxfxfdxxfxf ++=⋅⋅
∫
)(tg)(secln)(')(sec
9)
[ ]
( ) ( )
[ ]
Cxfxfdxxfxf +−=⋅⋅
∫
)(cotg)(cossecln)(')(cossec
10)
[ ] [ ] [ ]
Cxfdxxfxfgxf +=⋅⋅⋅
∫
)(sec)(')(t)(sec
11)
[ ] [ ] [ ]
Cxfdxxfxfxf +−=⋅⋅⋅
∫
)(cossec)(')(cotg)(cossec
12)
[ ] [ ]
Cxfdxxfxf +=⋅⋅
∫
)(tg)(')(sec
2
13)
[ ] [ ]
Cxfdxxfxf +−=⋅⋅
∫
)(cotg)(')(cossec
2
14)
[ ]
∫
+
⋅=⋅
+C
a
xf
a
dx
axf
xf )(
arctg
1
)(
)('
22
15)
[ ] [ ]
22
22
)( ,
)(
arcsen
)(
)(' axfC
a
xf
dx
xfa
xf <+
=⋅
−
∫
16)
[ ]
C
a
xf
a
dx
axfxf
xf +
⋅=⋅
−⋅
∫
)(
arcsec
1
)()(
)('
22
18)
[
]
[
]
[
]
[
]
)(')(ln)()(')()(')(
)(1)()(
xgxfxfxfxfxgyxfy
xgxgxg
⋅⋅+⋅⋅=⇒=
−
• Identidades trigonométricas
1) 1)(cos)(sen
22
=+ xx
2)
)(sec1)(tg
22
xx =+
3)
)(seccos1)(cotg
22
xx =+
4)
2
)2cos(1
)(sen
2
x
x−
=
5) 2
)2cos(1
)(cos
2
x
x+
=
6)
(a)sen(b).cos(b)sen(a).cosb)sen(a ±=±
7)
(b)sen(a).sen(b)cos(a).cosb)cos(a
m
=±
8)
−
+
=+ 2
ba
.cos
2
ba
2.sensen(b)sen(a)
9)
+
−
=− 2
ba
.cos
2
ba
2.sensen(b)sen(a)
10)
−
+
=+ 2
ba
.cos
2
ba
2.cos(b)coscos(a)
11)
−
+
−=− 2
ba
.sen
2
ba
2.sen(b)coscos(a)