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if xe y e x then dy dx is
Question:
if
$(xe)^y = e^x$
, then
$\frac{dy}{dx}$
is =
KCET - 2020
KCET
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
$(x e)^{y}=e^{x}$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$
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