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Question
If xy = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
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Solution
We have xy = ex–y
Taking logarithm on both sides, we get
y log x = x – y
⇒ y(1 + log x) = x
i.e. y = `x/(1 + log x)`
Differentiating both sides w.r.t. x, we get\
`("d"y)/("d"x) = ((1 + logx) * 1 - x(1/x))/(1 + logx)^2`
= `logx/(1 + log x)^2`.
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