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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. \\  %Let $x = a + jb \in \complex$ be a complex number, where $a \in \reals$, and $b \in \reals$. \\  The complex derivative of $x = a + jb \in \complex$, $a,b \in \reals$, is defined as   \begin{align*} \begin{equation}  Dx = \frac{dx}{da} + j\frac{dx}{db}.  \end{align*} \end{equation}  \paragraph{Example 1.}  Given $x = a + jb \in \complex$, $a,b \in \reals$, What is $D|x|$? \\