# Compute the given derivatives d/dx(ex) x=e

Compute the given derivatives

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Step 1
We have to find

Let $y={e}^{x}$
Taking log on both sides, we get
$\mathrm{log}y=x$
Differentiate it with respect to x,
$\frac{1}{y}\frac{dy}{dx}=\frac{d}{dx}x$
$\frac{dy}{dx}=y$
$\frac{dy}{dx}={e}^{x}$...(1)
Step 2
Put $x=e$ in (1), we get
${\left(\frac{dy}{dx}\right)}_{x=e}={e}^{e}$