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\newcommand{\reals}{\mathbb{R}}  \newcommand{\complex}{\mathbb{C}}  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.derivative complex derivatives of functionals.  \\ Let $x = a + jb \in \complex$ be a complex number, where $a \in \reals$, and $b \in \reals$. \\  The derivative of x is defined as   \[  Dx = \frac{dx}{da} + j\frac{dx}{db}.  \]