Alternative Equation Formats

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MathML

\begin{array}{rcl} \partial {\hat{Y}}_{r c} / \partial {\hat{N}}_{r c} & = & 1 - ({\hat{N}}_{r \cdot} + {\hat{N}}_{\cdot c} - {\hat{N}}_{\cdot c} {\hat{N}}_{r \cdot} / \hat{N}) / \hat{N} \\ \partial {\hat{Y}}_{r c} / \partial {\hat{N}}_{a c} & = & - ({\hat{N}}_{r \cdot} - {\hat{N}}_{r \cdot} {\hat{N}}_{\cdot c} / \hat{N}) / \hat{N} \\ \partial {\hat{Y}}_{r c} / \partial {\hat{N}}_{r b} & = & - ({\hat{N}}_{\cdot c} - {\hat{N}}_{r \cdot} {\hat{N}}_{\cdot c} / \hat{N}) / \hat{N} \\ \partial {\hat{Y}}_{r c} / \partial {\hat{Y}}_{a b} & = & {\hat{N}}_{r \cdot} {\hat{N}}_{\cdot c} / {\hat{N}}^{2} \end{array}

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Math as LaTeX Source

\begin{eqnarray*} \partial {\widehat{Y}_{rc}} / \partial {\widehat{N}_{rc}} & = & 1 ~ - ~ \left( \widehat{N}_{r \cdot } ~ + ~ \widehat{N}_{\cdot c} ~ - ~ \widehat{N}_{\cdot c} ~ \widehat{N}_{r \cdot } ~ / ~ \widehat{N} \right) ~ / ~ \widehat{N} \\[0.1in] \partial {\widehat{Y}_{rc}} / \partial {\widehat{N}_{ac}} & = & - ~ \left( \widehat{N}_{r \cdot } ~ - ~ \widehat{N}_{r \cdot } ~ \widehat{N}_{\cdot c} ~ / ~ \widehat{N} \right) ~ / ~ \widehat{N} \\[0.1in] \partial {\widehat{Y}_{rc}} / \partial {\widehat{N}_{rb}} & = & - ~ \left( \widehat{N}_{\cdot c} ~ - ~ \widehat{N}_{r \cdot } ~ \widehat{N}_{\cdot c} ~ / ~ \widehat{N} \right) ~ / ~ \widehat{N} \\[0.1in] \partial {\widehat{Y}_{rc}} / \partial {\widehat{Y}_{ab}} & = & \widehat{N}_{r \cdot } ~ \widehat{N}_{\cdot c} ~ / ~ \widehat{N}^{~ 2} \end{eqnarray*}