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\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{center}
\begin{alignat*}{5}
f(x) &= e^{\,xtan(x)} \nonumber \nonumber \nonumber \nonumber \nonumber \\
\frac{d}{dx} &= e^{\,xtan(x)} \;&&\cdot \frac{d}{dx} && \biggl(xtan(x) \biggr) &&~ \\
~&= e^{\,xtan(x)} \;&&\cdot &&\biggl(x\frac{d}{dx}tan(x) &&+ tan(x)\frac{d}{dx}(x) &&\biggr) \\
~&= e^{\,xtan(x)} \;&&\cdot &&\biggl( xsec^{2}(x) &&+ tan(x)(1) &&\biggr) \\
~&= e^{\,xtan(x)} \;&&\cdot &&\biggl( \quad xsec^{2}(x) &&+ tan(x) &&\biggr) \\
\end{alignat*}
$= e^{\,xtan(x)} \, xsec^{2}(x) \,+\, e^{\,xtan(x)}tan(x) $
\end{center}
\end{document}