\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1}
\definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1}
\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
\begin{axis}[
x=1cm,y=1cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-0.5,
xmax=6.5,
ymin=-0.25,
ymax=6.6,
xtick={-4,-3,...,6},
ytick={0,...,6},]
\clip(-4.66270591911281,-2.4761462907710943) rectangle (11.894647164540304,7.830725732214009);
\draw [-latex,line width=1pt, color=red] (0,0) -- (5,2);
\draw [-latex,line width=1pt, color=blue] (0,0) -- (1,4);

\draw [-latex,line width=1pt, color=red, dashed] (1,4) -- (6,6);
\draw [-latex,line width=1pt, color=blue, dashed] (5,2) -- (6,6);

\draw [-latex,line width=2pt, color=orange] (0,0) -- (6,6);

\begin{scriptsize}
\draw[color=red] (2.5189255735382816,1.3) node {$\overrightarrow{x}$};
\draw[color=blue] (0.25,2.142145794294401) node {$\overrightarrow{y}$};
\draw[color=orange] (2.4,3.158919254505808) node {$\overrightarrow{x+y}$};
\draw[color=red] (3.524996155221147,5.3) node {$\overrightarrow{x'\;\,}$};
\draw[color=blue] (5.9,4) node {$\overrightarrow{y'\;\,}$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}
\end{document}