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If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))...

If `y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))`, then `(dy)/(dx)=`

A

`(y^(3)-x)/(2y^(2)-2xy+1)`

B

`(x+y^(3))/(2y^(2)-x)`

C

`(y+x)/(y^(2)-2x)`

D

`(y^(2)-x)/(2y^(3)-2xy-1)`

Text Solution

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The correct Answer is:
D
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