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Calculus Review: Derivatives, Rules, Limits

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of
Review
section
3
ˋ
ˋ
-
3 0
.
Devivatives
(d)
'
lxn )
of Basic Enctims
=
(d)
'
=
'
@S
'
(Siuxj
=
X
)
=
cotxi
(Secx
'
(ix)
( Se
ix)
( lnlxl )
=
@s
"
)
'
'
=
g
=
X )
=
'
x )
'
=
'
=
(C)
(taux )
=
'
=
'
'
=
'
=
(cscx )
=
(taix )
( 109
'
=
'
a
X
)
=
Basic
Diffeventid
l.la fx ) )
2
3
4
5
.
(
'
fcx) ± g
=
'
IX)
)
( fcx ) g … )
.
.
.
.
(
(
我)
g
…
'
g
'
)
=
'
)
=
=
'
=
Rules
ǎfcgcx
The Chaiu Rule
1
2
ǎfcax
.
3
4
⻮
.
.
[ (f…
=
"
)
ǎlhfcxi
d
.
d
5、
)
x
]
=
)
( lnlfcx ) 1
=
)
=
ddxflgl.hn/)))=
)
)
=
Ex
Computeǎ
xtxt.xEX.com
:
pute
⻮ (4
3
"
)
、
Ex :
Ex
:
Comput
Compute
lnllogzllogxt
ǎtaicx
3
)
。
1)
)
Implicit
Exi
Diffeveutiatiou
Logavithmic
Exi
Compute
Differeutiatim
ǎ
lhx )
""
for
X
>
1
,
Exi
Special Limits
lim
x→
Ex
:
o
limosx
Sinx
X
l.im
x→ o
X→
"
1
-
⼼ )
WSX
o
lim
-1
X )
X
-
Ex :
lim
xsi
cosx
X
o
Sin ( X
X
2
-1
2
-
1
tx -2
)
e
=
lim
Cltxi
xsoe-li.nl
1
⼗点
X-e-liw.CI
Exi
i
ixse-l.im
(
n
) 的
-
⼗
1⼗
六
六 )
"
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