If \( y \log x=(x-y) \), prove that \( \frac{d y}{d x}=\frac{\log x}{(1+\log x)^{2}} \)

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If \( y \log x=(x-y) \), prove that \( \frac{d y}{d x}=\frac{\log x}{(1+\log x)^{2}} \)
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