#### Answer

\[{y^,} = x{e^x} + {e^x}\]

#### Work Step by Step

\[\begin{gathered}
y = x{e^x} \hfill \\
Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,the\,\,derivative \hfill \\
{y^,} = \,\left( x \right)\,{\left( {{e^x}} \right)^,} + \left( {{e^x}\,} \right)\,{\left( x \right)^,} \hfill \\
Then \hfill \\
{y^,} = x\,\left( {{e^x}} \right) + {e^x}\,\left( 1 \right) \hfill \\
Multiplying\, \hfill \\
{y^,} = x{e^x} + {e^x} \hfill \\
\end{gathered} \]