Page 114 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math6-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV
dy 1
dy dx f ′ ()
x
uksV~l 1 ( 1
dy 2 dy 2 f 2 ′ () x
dx
dy 1 y 1 x

vr% (
dy 2 y 2 x

D;k vki tkurs gSa lkè;µfdlh iQyu dk fdlh nwljs iQyu osQ lkis{k vody&xq.kkad izFke iQyu dk
osQ lkis{k vody&xq.kkad vkSj nwljs iQyu dk osQ lkis{k vody&xq.kkad dk
vuqikr gksrk gSA

gy lfgr mnkgj.k

1

mnkgj.k 1- dk vody&xq.kkad
osQ lkis{k ij Kkr dhft,A
2
1
−
1
d (tan x ) 1 + x 2 1 − x 2
gy % =
d (sin − 1 ) x 1 1 + x 2
1 − x 2
1 3
1 −
1 4 2 23
( ij ( ( = . mÙkj
2 1 + 1 5 5
4 4
mnkgj.k 2- dk vody&xq.kkad
osQ lkis{k Kkr dhft,A
gy % ekuk ( rFkk (

d tan x

;gk¡ ( e (
dx
d
vkSj ( dx sin x = cos x

dy 1 de tan x e tan x .sec x e tan x
2
vr% ( = = . mÙkj
3
dy 2 d sin x cos x cos x
1+ x 2 −1
mnkgj.k 3- tan −1 dk vody&xq.kkad tan −1 x osQ lkis{k Kkr dhft,A
x

1 + x − 2 1
−
gy % ekuk ( tan − 1 x rFkk ( tan x
1