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\documentclass[10pt,a4paper,final]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\begin{document}
\begin{math}
\begin{array}
\frac {\mathrm{d}\left( {{\mathrm{[Lext]}} \, \cdot \, {V}_{c} } \right) } {\mathrm{d}{t} } \; &=& \; { \, - \, {V}_{c} \, \cdot \, \left( {{\mathrm{kAX}} \, \cdot \, {\mathrm{[Lext]}} } \right) } \\
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l.13 \frac
{\mathrm{d}\left( {{\mathrm{[Lext]}} \, \cdot \, {V}_{c} } \right...
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! LaTeX Error: Illegal character in array arg.
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...
Thanks,