if ((xe)^y = e^x), then (\frac{dy}{dx}) is = | Mathematics | SolveeIt

if $(xe)^y = e^x$ , then $\frac{dy}{dx}$ is =

$\frac {log x}{ (1+logx)^2}$

$\frac {1}{ (1+logx)^2}$

$\frac {log x}{ (1+logx)}$

$\frac {e^x}{ x(y-1)}$

Answer

$\frac {log x}{ (1+logx)^2}$

Explanation

$(x e)^{y}=e^{x}$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$

Mathematics Question on Derivatives of Functions in Parametric Forms