Question

$x^{y} = e^{x}$
find dy/dx ??
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Answer 1

$\sf \: x^{y} = e^{x} \\ \sf \: differenciating \: w.r.t.x \\ \sf \frac{d}{dx} ( {x}^{y} ) = \frac{d}{dx} ( {e}^{x} ) \\ \sf {x}^{y} ( \frac{y}{x} + log(x) \frac{dy}{dx} ) = {e}^{x}$

$\sf\frac{dy}{dx} = (\frac{ {e}^{x} }{ {x}^{y} } - \frac{y}{x} ) \frac{1}{ log(x) }$

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