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Inverse of a Function

if xy=ex-y, t...

Question

$i f x^{y} = e^{x - y}, t h e n \frac{d y}{d x}$ =

A

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C

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Solution

The correct option is C
$x^{y} = e^{x - y} i . e . y l n x = x - y i . e . y = \frac{x}{1 + l n x} ∴ \frac{d y}{d x} = \frac{l n x}{(1 + l n x)^{2}}$

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