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  4. If y = ex +ex+ex+..∞, then (dy/dx) =

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Q. If $y = e^{x +e^x+e^x+..\infty}, $ then $\frac{dy}{dx} = $

Limits and Derivatives

Solution:

$y =e^{x+y}\Rightarrow \frac{dy}{dx} = e^{x+y} \left(1+ \frac{dy}{dx}\right)$
$ \Rightarrow \frac{dy}{dx} \left(1-e^{x+y}\right) = e^{x+y} $
$\Rightarrow \frac{dy}{dx} = \frac{e^{x+y}}{1-e^{x+y}} = \frac{y}{1-y} $