HOSILA

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Mavzu: HOSILA
REJA

1. Hosila ta’rifi.

2. Hosilaning geometrik
ma’nosi.

3. Hosilaning mexanik ma’nosi.

4. Hosila jadvali.

HOSILA TA’RI FI
Argument
orttirmasi Ta’rif . Funksiya orttirmasining argument
orttirmasiga nisbatining , argument orttirmasi
nolga intilgandagi limitini f(x) funksiyaning x
o
nuqtadagi hosilasi deyiladi.
∆
x ∆
y
x
o x
o + x∆ xy
O∆ x = x - x
o F u n k s iy a o r ttir m a s i
∆ y = f(x) - f(x
o )=f(x
o + x)-f(x
∆
o )
x
x f x x f
x
y
x f
x x
o

  




   
) ( ) (
lim lim ) ('
0 0

HOSILA JADVALI.
1
)' (ln ) 7
,
ln
1
)' (log ) 6
, ln ) ( ) 5
, )' ( ) 4
)' ( ) 3
, 1 ' ) 2
, 0 ' ) 1
1
x
x
a x
x
a a a
e e
x c x
x
с
a
x x
x x
c c




 



.
sin
1
)' ( ) 12
,
cos
1
)' ( ) 11
sin )' (cos ) 10
, cos )' (sin ) 9
,
2
1
)' ( ) 8
2
2
x
ctgx
x
tgx
x x
x x
x
x
 

 



HOSI LAN IN G GEOMETRI K
MA’N OSIU
R
I N
M
A
f(x) funksiyaning x
o nuqtadagi hosilasi , f(x)
funksiya grafigiga x
o nuqtasidan o’tkazilgan
urinmaning Ox o’qining musbat yo’nalishi bilan
hosil qilgan burchak tangensiga teng.
Y =f(x )
x
o xy
O αf ΄ (x
o ) = tg α
f (x) = x -2
f ʹ ( x) = tg45 o
=1

HOSILAN IN G MEX AN IK
MA’N OSI
S(t ) qonuniyat bilan harakatlanayotgan
moddiy nuqtaning t
o momentdagi oniy tezligi ,
S(t) yo’ldan vaqt bo’yicha birinchi tartibli
hosilasiga teng:
V(t
o ) =S ʹ (t
o )
S (t) = 3t 2
+4t+3, v(t)-? , a (t) -?
v ( t) =(3t 2
+4t+3) ʹ =6t+4, a (t)=(6t+4) ʹ =6.S ΄ (t) = V (t) – tezlik ,
S ΄΄ (t) = v ΄ (t) = a (t) – tezlanish .

     
  x x x x x x x x x
x x x x f x x f y
topiladi orttirmasi funksiya Yechish
toping hosilani x y
           
         

) 2 ( ) (
: .
. . 1
2 2
2
  x y Jav x x x x
x
x x x
x
y
y
x
x x
2 ' . . 2 ) 0 2 ( 2
) 2 (
lim
lim lim
0
0 0
0
0 0
      


   



 
 
   Funk siy aning
hoslasini
t a’rif bo’y icha t oping.
Funk siy aning hoslasini t a’rif bo’y icha
t oping.
1. y=4x+3 2. y=x 3

17. . 17 1 32 48
1 ) 2 ( 16 ) 2 ( 12 ) 2 ('
1 16 12
0 1 8 2 4 3
)' 3 8 4( '
:
? ) 2 (' , 3 8 4 . 2
. 4 ' .
0 4 )' 8 4( '
:
. 8 4 . 1
2
2
1 2 1 3
2 3
2 3
Jav
y
x x
x x
x x x y
Yechish
y x x x y
y Jav
x y
Yechish
x y
   
        
  
      
    
     

   
 
 
. ? ) 1 (' , 3 . 4
? ) 2(' , 2
2
1
2, 0 . 3
? ' , 1 4 2 2 . 2
, ? ) 3 (' , 6 5 . 1
. )' (
4
2 2
2 4
2
1
  
   
    
   
 

y x y
y x x y
y x x y
y x y
x x
 
NAMUNA YORDAMIDA
1 - VAZIFAHI BAJARAMIZ
DARAJALI
fUNKSIYA
HOSILASINI
HISOBLANG

.
12
1
) 20 (' .
.
12
1
4
1
3
1
2
3
1
2
3
1
8
3
1
) 12 20(
3
1
) 20('
, ) 12 (
3
1
) 12 (
3
1
)' ) 12 (( ) ('
:
? ) 20 (' . 12 ) ( . 1
2 3
2 3 3
2
3
2
3
2 1 3
1
3
1
3

           
     
  

  
 
f Jav
f
x x x x f
Yechish
f x x fMUSTAQIL
YECHING
. ? ' , . 6
? ' , 3 cos 3 sin . 5
. ? ) 7 (' , 3 . 4
? ) 2 (' , 2
4
1
5, 0 . 3
? ' , 5 2 . 2
, ? ) 1 (' , 6 25 . 1
2 2
2 2
2 3
2
  
  
  
   
   
  
y ctgx tgx y
y x x y
y x y
y x x x y
y x x y
y x x y

. ? ) 35 (' , 3 . 4
, ? ) 2 (' , 2 4 . 3
? ) 1(' , 6 5 . 2
, ? ) 3 (' , 2 8 2 . 1
5
3
3
2
  
  
  
    
y x y
y x x y
y x x y
y x x yUYGA VAZIFA
I. BUGUN NIMALARNI
O’RGANDIM ?
II. HOSILANI
HISOBLANG

BUGUN NIMALARNI O’RGANDIM ?

1. Hosila ta’rifi.

2. Hosilaning geometrik
ma’nosi.

3. Hosilaning mexanik ma’nosi.

4. Hosila jadvali.

GURUX TO’PLAGAN
BALLAR
1-guruh bal
2-guruh bal
3-guruh bal

1. Карп А.П. Сборник задач по алгебре
началом анализа. Учебное пособие для
учашихся школ и классов с углебленным
изучением математики. М.:Просвещение ,
1995.
2. Дорофеев Г.В. ,Кузнецова Л.Я.,СедоваЕ.А.
Алгебра и начала анализа. 10 кл. Задачник
для общеобразоват. Учреждений. М.:Дрофа ,
20 0 8 . ADABIYOTLAR

Mavzu: HOSILA REJA  1. Hosila ta’rifi.  2. Hosilaning geometrik ma’nosi.  3. Hosilaning mexanik ma’nosi.  4. Hosila jadvali.

HOSILA TA’RI FI Argument orttirmasi Ta’rif . Funksiya orttirmasining argument orttirmasiga nisbatining , argument orttirmasi nolga intilgandagi limitini f(x) funksiyaning x o nuqtadagi hosilasi deyiladi. ∆ x ∆ y x o x o + x∆ xy O∆ x = x - x o F u n k s iy a o r ttir m a s i ∆ y = f(x) - f(x o )=f(x o + x)-f(x ∆ o ) x x f x x f x y x f x x o             ) ( ) ( lim lim ) (' 0 0

HOSILA JADVALI. 1 )' (ln ) 7 , ln 1 )' (log ) 6 , ln ) ( ) 5 , )' ( ) 4 )' ( ) 3 , 1 ' ) 2 , 0 ' ) 1 1 x x a x x a a a e e x c x x с a x x x x c c          . sin 1 )' ( ) 12 , cos 1 )' ( ) 11 sin )' (cos ) 10 , cos )' (sin ) 9 , 2 1 )' ( ) 8 2 2 x ctgx x tgx x x x x x x       

HOSI LAN IN G GEOMETRI K MA’N OSIU R I N M A f(x) funksiyaning x o nuqtadagi hosilasi , f(x) funksiya grafigiga x o nuqtasidan o’tkazilgan urinmaning Ox o’qining musbat yo’nalishi bilan hosil qilgan burchak tangensiga teng. Y =f(x ) x o xy O αf ΄ (x o ) = tg α f (x) = x -2 f ʹ ( x) = tg45 o =1

HOSILAN IN G MEX AN IK MA’N OSI S(t ) qonuniyat bilan harakatlanayotgan moddiy nuqtaning t o momentdagi oniy tezligi , S(t) yo’ldan vaqt bo’yicha birinchi tartibli hosilasiga teng: V(t o ) =S ʹ (t o ) S (t) = 3t 2 +4t+3, v(t)-? , a (t) -? v ( t) =(3t 2 +4t+3) ʹ =6t+4, a (t)=(6t+4) ʹ =6.S ΄ (t) = V (t) – tezlik , S ΄΄ (t) = v ΄ (t) = a (t) – tezlanish .

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