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Pravila diferenciranja
( )
( ) '''
''
)2
)1
vuvu
uCuC
+=+
=
( )
( )
( )
2
'''
'''
'''
)5
)4
)3
)2
v
vuvu
v
u
vuvuvu
vuvu
vuvu
⋅−⋅=
⋅+⋅=⋅
−=−
+=+
Tablica izvoda nekih elementarnih funkcija
( ) .,0'
constCC −=
( ) Rnnxxnn
∈=−
,
1'
( ) xx
ee =
'
( ) xx cossin'
=
( ) aaaxx
ln'
=
( )2
'
1
1arcsin
x
x
−
=( ) Rnnxx ∈= ,
( )x
x
xx 2
1,
11 '
2
'
=−=
( )ax
x
a
ln
1log
'
⋅
=
( ) { }0/,1
ln'
Rxx
x ∈=
( ) xx cossin =
( ) xx sincos'
−=
( )x
tgx2
'
cos
1=
( )x
ctgx2
'
sin
1−=
21 x−
( )2
'
1
1arccos
x
x
−
−=
( )2
'
1
1
xarctgx
+
=
( )2
'
1
1
xarcctgx
+
−=
Primjer 1. Odrediti izvode sledećih funkcija:
( ) ( )xxyb
xxy
xxxy
xxxy
xxxya
3213)
289
289
122433
243)
22
2'
012'
111213'
23
+⋅+=
+−=
+−=
⋅+⋅−⋅=
+−=
−−− ( ) 1'
−
=nn
nxx
( ) ( )( )
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
( ) ( )
( ) ( )
xxy
xxxxxxxxy
xxxxxxy
xxxxy
xxxxy
xxxxy
vuvuvu
xxyb
2224
41812124121812
41433626
413326
0221332023
32133213
3213)
3'
3333'
22'
22'
122212'
'222
'2'
'''
+=
+++=+++=
⋅+⋅+⋅+⋅=
⋅+++⋅=
+⋅⋅+++⋅+⋅=
+⋅+++⋅+=
⋅+⋅=⋅
+⋅+=
−−
( ) ( ) ( ) ( )( )
( ) ( )( ) ( ) ( ) ( ) ( )( )( )
( ) ( )
2
''''
'
2
'
'
1ln11
ln1
1
1ln1lnln
1
1ln1ln
1
ln)
'
⋅−+⋅
⋅+⋅
+
+⋅−+⋅⋅+⋅=
+
+⋅−+⋅=
+=
xxxxx
x
xxxxxxxxy
x
xxxxxxy
x
xxyc
2
'''
v
vuvu
v
u ⋅−⋅=
( ) ( )
( )( ) ( )
( )
( )
( )2'
2
'
2
'
2
'
1
1ln
1
ln1lnln
1
ln11ln
1
1ln1ln1
+
++=
+
−+++=
+
−+⋅+=
+
⋅−+⋅
⋅+⋅
=
x
xxy
x
xxxxxxy
x
xxxxy
x
xxxx
xx
y
Zadaci za vježbu: Odrediti izvode sledećih funkcija
( ) ( )xxyd
xxyc
xxyb
xxxya
cos)
67)
46)
8435)
2
22
43
56
⋅=
+⋅−=
−=
−+−= Uputstvo:Koristiti tablicu
izvoda i osnovna pravila izvoda.
( ) xxxxyh
xxxyg
x
xyf
x
xxye
sin2cos2)
cossin)
ln)
1
1)
2
2
2
2
⋅+⋅−=
+⋅=
=
+
+−=
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