If x^{y} = e^{x−y} , then `dy/dx` = ______

A) `(1+x)/(1 + log x)`

B) `log x/(1 + log x)^2`

C) `(1 - log x)/(1 + log x)`

D) `(1-x)/(1 + log x)`

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#### Solution

x^{y} = e^{x − y}

Taking logarithm on both sides, we get

ylog x = (x − y) log e = x − y

∴ `y = x/(1 + log x)`

Differentiating w.r.t. x, we get

Concept: Continuity of Some Standard Functions - Trigonometric Function

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