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\newcommand{\reals}{\mathbb{R}}  \newcommand{\complex}{\mathbb{C}}  \subsubsection{Complex derivative}  \paragraph{Complex derivative}  Here we provide a definition for the 'complex' derivative of a real-valued function $f : \complex^n \to \reals$ with respect to its complex variables. \\  The complex derivative of $x = a + jb \in \complex$, $a,b \in \reals$, is defined as