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Question
If xy = ex−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)`
Solution
xy = ex − 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
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Continuity of Some Standard Functions - Trigonometric Function
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