#### Answer

\[y = 2x - e\]

#### Work Step by Step

\[\begin{gathered}
y = x\ln x \hfill \\
Evaluate\,\,the\,\,function\,\,at\,\,x = e \hfill \\
y = \,\left( e \right)\ln \,\left( e \right) \hfill \\
y = e\,\,,\,\,Point\,\,\left( {e,e} \right) \hfill \\
Find\,\,the\,\,deriva\,tive\,\,of\,\,the\,\,function \hfill \\
{y^,} = \,\,{\left[ {x\ln x} \right]^,} \hfill \\
{y^,} = x\,\left( {\frac{1}{x}} \right) + \ln \,\left( x \right)\,\left( 1 \right) = 1 + \ln x \hfill \\
Evaluate\,\,{y^,}\,\left( e \right) \hfill \\
{y^,} = 1 + \ln \,\left( e \right) = 2 \hfill \\
m = 2 \hfill \\
Use\,\,the\,\,point\, - slope\,\,form \hfill \\
y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\
y - e = 2\,\left( {x - e} \right) \hfill \\
y = 2x - e \hfill \\
\end{gathered} \]