deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 289730b..3d7f339 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\frac{\partial (Ax)}{\partial x_1} = \left[ \begin{array}{c}  \frac{\partial (Ax)_1}{\partial x_1} \\ \vdots \\ \frac{\partial (Ax)_m}{\partial x_1}  \end{array} \right]  = \left[ \begin{array}{c} A_{11} \\ \vdots \\ A_{m1} \end{array} \right]. \nonumber  \end{equation}  Using the expression above, we write the derivative of $Ax$ as  \begin{eqnarray} \begin{equation}  D(Ax) = \left[ \begin{array}{ccc}  \frac{\partial (Ax)_1}{\partial x_1} & \cdots & \frac{\partial (Ax)_1}{\partial x_n} \\  \vdots & \vdots & \vdots \\ 
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A_{11} & \cdots & A_{1n} \\  \vdots & \vdots & \vdots \\  A_{m1} & \cdots & A_{mn}  \end{array} \right]  \end{eqnarray} \right]. \nonumber  \end{equation}