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

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