Ð_o hàm và vi phân
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7/25/2019 _o Hm V Vi Phn
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O HM V VI PHN.
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7/25/2019 _o Hm V Vi Phn
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O HM TI 1 IM
Cho y = f(x) xc nh trong (a, b) x, x!t t" #$
0 0 0 0
0
( ) ( ) ( ) ( ) ( )f x f x f x f x x f x
x x x x
+ = =
%&' t" #$ trn c g*+* hn h-' hn .h* x /x
hay x / th0 f c o h2 t* x3
4t
0
00
( 0)
( )( ) lim
x xx
f xf x
x
=
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7/25/2019 _o Hm V Vi Phn
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0( )
tan
f x
x
=
0tan ( )f x =
x x
f5(x) 6 h7 #$ gc t*&8 t'y&n c9a :;ng cong
(C)< y = f(x) t* t*&8 *2 M(x, f(x))
x
f(x)
x x
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7/25/2019 _o Hm V Vi Phn
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o h2 tr* t* x* t* xng cFng thAc o h2 cc h2 2+*
( )
( )
( )
( )
2
2
2
2
1arcsin
1
1arccos
1
1arctan
1
1arccot
1
xx
xx
xx
x
=
=
=
+ = +
( )
( )
( )
( )
2
2
cosh sinh
sinh cosh
1tanh
cosh
1cothsinh
x x
x x
xx
xx
=
=
=
=
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7/25/2019 _o Hm V Vi Phn
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o h2 h2 cho th^o tha2 #$
Cho cc h2 #$ < ( )
( )
x x t
y y t= =
%&' < _ x = x(t) c h2 ng:Kc t = t(x)
_ x(t) G y(t) c o h2, x5(t) `
( ) ( ). ( )y x y t t x =
( )( )
( )
y ty x
x t
=
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7/25/2019 _o Hm V Vi Phn
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S? D
Cho n
[ ]
[ ]
( )
( )
sin( )
c
sin2
co) s2
os(
n
n
n
n
ax b
ax
a ax
b
b n
a ax b n
+ = + +
= + ++
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7/25/2019 _o Hm V Vi Phn
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CFng thAc o h2 c8 cao
( )( ) ( ) ( )n n nf g f g =
( )( ) ( ) ( )
0
.
nn k k n k
nk
f g C f g
==
(cFng thAc ^*bn*t)
o h2 c8 cao
c9a tJng h*7' G* th^o x (b*&n c 6e8)* :a GR DtL(chU t?nh &n c8 L)
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