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\end{equation}  Using the expression above, we write the derivative of $Ax$ as  \begin{eqnarray}  D(Ax) &=& =  \left[ \begin{array}{ccc} \frac{\partial (Ax)_1}{\partial x_1} & \cdots & \frac{\partial (Ax)_1}{\partial x_n} \\  \vdots & \vdots & \vdots \\  \frac{\partial (Ax)_m}{\partial x_1} & \cdots & \frac{\partial (Ax)_m}{\partial x_n}  \end{array} \right]  &=& =  \left[ \begin{array}{ccc} A_{11} & \cdots & A_{1n} \\  \vdots & \vdots & \vdots \\  A_{m1} & \cdots & A_{mn}