[Tex/LaTex] How continue an equation next line

Question

How can continue the equation of the rectangle red in next line?

\documentclass[11pt,a4paper,twocolumn]{article}

...

\begin{equation*}
    \left| \dot{r} \right| =
    \sqrt{{- \, {e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {{e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {(- \, {e}^{-t})}^{2}}
\end{equation*}

Answer 1

I suggest using the multlined environment from mathtools to break the radicand . You also can choose not to break it, but to type in medsize (~80 % of \displaystyle) with the \mediummath command from nccmath. I took the opportunity to clean your code:

\documentclass[11pt,a4paper,twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools, nccmath}

\begin{document}

\begin{equation*}
    \bigl| \dot{r} \bigr| =
    \sqrt{\begin{multlined}[b] -\!\bigl(e^{-t} ( \cos t + \sin t )\bigr)^2 + \\ \bigl(e^{-t} (\cos t + \sin t)\bigr)^2 + \bigl(-e^{-t}\bigr)^2 \end{multlined}}
\end{equation*}
\begin{align*}
    \bigl| \dot{r} \bigr| & =
    \sqrt{\medmath{ -\!\bigl(e^{-t} ( \cos t + \sin t )\bigr)^2 + \bigl(e^{-t} (\cos t + \sin t)\bigr)^2 + \bigl(-e^{-t}\bigr)^2}} \\
         & = \sqrt{ -\!\bigl(e^{-t} ( \cos t + \sin t )\bigr)^2 + \bigl(e^{-t} (\cos t + \sin t)\bigr)^2 + \bigl(-e^{-t}\bigr)^2}
\end{align*}

\end{document}