If xy=ex−y, prove that dxdy=(1+logx)2logx.

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{If } {x}^{{{y}}}={e}^{{{x}-{y}}}, { prove that } {{{.{d}{y}.}

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$If x^{y} = e^{x - y}, prove that \frac{d y}{d x} = \frac{lo g x}{( 1 + lo g x ) ^{2}} .$

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If x^{y} = e^{x - y}, prove that \frac{d y}{d x} = \frac{lo g x}{( 1 + lo g x ) ^{2}} .

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Question Text

If x^{y} = e^{x - y}, prove that \frac{d y}{d x} = \frac{lo g x}{( 1 + lo g x ) ^{2}} .