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

Explanation

To prove that \(\frac{dy}{dx} = \frac{y}{2y - x}\) for the function \(y = x + \frac{1}{x + \frac{1}{x + \frac{1}{x + \cdots}}}\), we can follow these steps:

### Step 1: Define the function
We start with the equation:
\[ y = x + \frac{1}{y} \]
This is because the continued fraction representation of \(y\) implies that the entire expression can be replaced by \(y\) itself.
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