If Xy = Ex−Y , Then Dy/Dx - Mathematics and Statistics

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

Concept: Continuity of Some Standard Functions - Trigonometric Function
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