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If y=x+1/(x+1/(1/(x+))), prove that (dy)...

If `y=x+1/(x+1/(1/(x+)))`, prove that `(dy)/(dx)=y/(2y-x)`

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`y=x+1/(x+1/(1/(x+)))`
`y=x+1/y`
`y-1/y=x`
`frac{dy}{dx}+1/yfrac{dy}{dx}=1`
`frac{dy}{dx}[frac{y^2+1}{y^2}]=1`
`frac{dy}{dx}=frac{y^2}{1+y^2}=>frac{y/(y+(1/y))}`
Since, `1/y=y-x`
`frac{dy}{dx}=frac{y}{2y-x}`
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