If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo...

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)`

Text Solution

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`y=sqrt(sinx+sqrt(sinx+sqrt(sinx+......oo)))`
`therefore y^(2)=sinx+sqrt(sinx+sqrt(sinx+......oo))`
`therefore y^(2)=sinx+y`
Differentiating both sides w.r.t. x, we get,
`2y(dy)/(dx)=cosx+(dy)/(dx)`
`therefore (2y-1)(dy)/(dx)=cosx`
`therefore (dy)/(dx)=(cosx)/(2y-1)`

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If y=sqrt(sinx+sqrt(sinx+sqrt(sinx..." to "oo)))," then "(2y-1)y_(1)=

`sinx`

`-cosx`

`-sinx`

`cosx`

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . .oo))) , then (dy)/(dx) is equal to

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

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

`(2x-1)/(cosy)`

`(cosy)/(2x-1)`

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+...,))) , then dy/dx is equal to

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

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

`y^2/(cosx-x)`