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"If "y=x + (1)/(x + (1)/(x + (1)/(x+......

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

Text Solution

Verified by Experts

We have
`y=x + (1)/(x + (1)/(x + (1)/(x+....)))=x+(1)/(y)`
`or y^(2)=xy+1`
` or 2y(dy)/(dx)=y+x(dy)/(dx)+0" [Differentiating both sides w.r.t.x]"`
`or (dy)/(dx)(2y-x)=y`
`or (dy)/(dx)=(y)/(2y-x)`
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