Question

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)`

Answer 1

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