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If y=sqrt(sinx+y),then (dy)/(dx)dot...

If `y=sqrt(sinx+y),then (dy)/(dx)dot`

A

`(cosx)/(2y-1)`

B

`(cosx)/(1-2y)`

C

`(sinx)/(1-2y)`

D

`(sinx)/(2y-1)`

Text Solution

Verified by Experts

`:' y = (sinx+y)^(1//2)`
` :. (dy)/(dx) = 1/2 (sinx+y)^(-1//2).(d)/(dx)(sin x+y)`
`rArr (dy)/(dx) = 1/2.(1)/((sinx+y)^(1//2)).(cosx+(dy)/(dx))` , `[:' (sinx+y)^(1//2) = y]`
`rArr (dy)/(dx) (1-(1)/(2y))= (cosx)/(2y)`
`:. (dy)/(dx) = (cosx)/(2y).(2y)/(2y-1)=(cosx)/(2y-1)`
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