Page 94 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math4-1 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 −1 dy
mnkgj.k 2- ;fn y= x sin x rks dk eku Kkr dhft,A
dx

gy % : x sin − 1 x
nksuksa i{kksa dk * ysus ij
* : log x sin − 1 x = sin − 1 x . log x

osQ lkis{k vodyu djus ij
1 dy : sin − 1 x . 1 + log . 1
x
y dx x 1 − x 2

dy : y   1 .sin − 1 x + 1 .log x  
dx  x 1 − x 2 
 

dy − 1  1 1 
∴ : x sin x  sin − 1 x + . log x  mÙkj
dx  x 2 
 1 − x 

mnkgj.k 3- iQyu % dk osQ lkis{k vody xq.kkad Kkr dhft,] tcfd % ,d vpj gSA
gy % eku yks : -
nksuksa i{kksa dk y?kqx.kd ysus ij
* : * -

;k * : * -
;k * :

nksuksa i{kksa dk vodyu djus ij
1 dy :
.
y dx
dy :
dx

: - j[kus ij
dy : -

dx mÙkj
1
mnkgj.k 4- iQyu dk osQ lkis{k vodyu dhft,A
x
b
a
x
(+ ) ( + ) (+ ) c
x
1
gy % eku yhft, :
) ( +
(x + ax b ) (x + ) c
nksuksa i{kksa dk y?kqx.kd ysus ij
1
* log
(x + ax b ) (x + ) c
) ( +