\begin{tikzpicture}
  \begin{axis}[
    xlabel = $x$, ylabel = $y$,
    width = 10cm, height=6cm,
    axis lines = middle,
    grid,
    xmin=-1.5, xmax=5.5,
    ymin=-1.5, ymax=1.5,
    legend pos=outer north east,
    samples=10000
  ]

    \addplot+ [
      no marks,
      domain = 0:5.5,
    ]{sin(deg(sqrt(x) * (e^(x))))};
    \addlegendentry{$y=sin(\sqrt{x}e^x)$}
    
  \end{axis}
\end{tikzpicture}