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If y=sqrt(logx+sqrt(cosx+sqrt(cosx+...to...

If `y=sqrt(logx+sqrt(cosx+sqrt(cosx+...tooo))),` prove that `(dy)/(dx)=(sinx)/(1-2y)`

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