Question:
if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =
if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =
Updated On: May 19, 2024
- $\frac {log x}{ (1+logx)^2}$
- $\frac {1}{ (1+logx)^2}$
- $\frac {log x}{ (1+logx)}$
- $\frac {e^x}{ x(y-1)}$
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The Correct Option is A
Solution and Explanation
$(x e)^{y}=e^{x}$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$
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