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If y=e^(x+e^(x+e^(x+dotto\ oo))) , show ...

If `y=e^(x+e^(x+e^(x+dotto\ oo)))` , show that `(dy)/(dx)=y/(1-y)` .

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Verified by Experts

Given that,
`y=e^(x+e^(x+e^(x+dotto\ oo)))`
`y=e^(x+y)`
`=>logy=log e^(x+y)`
`=>logy=(x+y) log e`
`=>logy=(x+y) `
`1/y(dy)/(dx)=1+(dy)/(dx)`
`=>(dy)/(dx)(1/y-1)=1`
`(dy)/(dx)=y/(1-y)`
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