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\end{equation}  Using the expression above, we write the derivative of $Ax$ as  \begin{eqnarray}  D(Ax) &=& \left[ \frac{\partial (Ax)}{\partial x_1}, \dots, \frac{\partial (Ax)}{\partial x_n} \right]\nonumber\\  &=& \left[ \begin{array}{ccc}  \frac{\partial (Ax)_1}{\partial x_1} & \cdots & \frac{\partial (Ax)_1}{\partial x_n} \\  \vdots & \vdots & \vdots \\