Given: xy = e^{(x – y)}

Taking log on both sides, we get

log (xy) = log (e^{(x – y)})

⇒ log x + log y = (x - y) log e

⇒ log x + log y = (x - y) .1

⇒ log x + log y = (x - y)

Now, differentiate both sides with respect to x