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Suppose $f: \complex^n \to \reals$ is a real-valued function defined for $x \in \complex^n$. The derivative $Df(x)$ is defined as \\  \begin{equation}  \label{eqn:derivative}  Df(x) = \left[ \frac{\partial f}{\partial x_i}(x), x_1}(x),  \dots, \frac{\partial f}{\partial x_n}(x) \right]. \end{equation}  \paragraph{Example 3.}