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"If "e^(y)(x+1)=1," show that "(d^(2)y)/...

`"If "e^(y)(x+1)=1," show that "(d^(2)y)/(dx^(2))=((dy)/(dx))^(2).`

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`e^(y)(x+1)=1`
`impliese^(y)=(1)/(x+1) " " ` ...(1)
Differentiate both sides w.r.t. x
`e^(y)(dy)/(dx)=(-1)/((x+1)^(2))`
`implies(1)/(x+1)(dy)/(dx)= -(1)/((x+1)^(2)) " " ` From equation (1)
`implies (dy)/(dx)=-(1)/(x+1)`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)(-(1)/(x+1)) = (1)/((x+1)^(2))=(-(1)/(x+1))^(2)=((dy)/(dx))^(2)`
` " " ` Hence Proved.
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