Alternative Equation Formats

$$\begin{array}{rc}\frac{\mathrm{\partial <!--\; \partial \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}{p}_o(Y=i|\mathbf{x})}{\mathrm{\partial <!--\; \partial \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}=& \{\begin{array}{ll}{F}^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_1+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_1(\mathbf{x})& i=1\\ F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i(\mathbf{x})-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>1}+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>1}(\mathbf{x})& i=2,\dots <!--\; \dots \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>,k\\ -<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k(\mathbf{x})& i=k+1\end{array}\end{array}$$

$$\begin{array}{rc}\frac{\mathrm{\partial <!--\; \partial \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}{p}_o(Y=i|\mathbf{x})}{\mathrm{\partial <!--\; \partial \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}=& \{\begin{array}{ll}{F}^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_1+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_1(\mathbf{x})& i=1\\ F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i(\mathbf{x})-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>1}+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>1}(\mathbf{x})& i=2,\dots <!--\; \dots \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>,k\\ -<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>F^{\prime }({\mathrm{\alpha <!--\; \alpha \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k+{\mathbf{x}}^{\prime }{\mathit{\beta <!--\; \beta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_s){\mathit{\delta <!--\; \delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k(\mathbf{x})& i=k+1\end{array}\end{array}$$

\begin{eqnarray*} \frac{\partial p_ o(Y=i|\mb{x})}{\partial {\bbeta }} = & \left\{ \begin{array}{ll} F'(\alpha _{1}+\mb{x}'{\bbeta _{s}})\bdelta _1(\mb{x}) & i=1 \\ F'(\alpha _{i}+\mb{x}'{\bbeta _{s}})\bdelta _ i(\mb{x}) - F'(\alpha _{i-1}+\mb{x}'{\bbeta _{s}})\bdelta _{i-1}(\mb{x}) & i=2,\ldots ,k \\ -F'(\alpha _{k}+\mb{x}'{\bbeta _{s}})\bdelta _{k}(\mb{x}) & i=k+1 \end{array} \right. \end{eqnarray*}