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

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

Discussion

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