Alternative Equation Formats

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MathML

\begin{array}{rcl} \log (- ϕ^{'} (u_{k})) & = & \log (\frac{1}{α} {(- \log u_{k})}^{\frac{1}{α} - 1} \frac{1}{u_{k}}) \\ = & - \log α - \log (u_{k}) + (\frac{1}{α} - 1) \log (- \log (u_{k})) \\ \frac{d \sum_{k} \log (- ϕ^{'} (u_{k}))}{d α} & = & \sum_{k = 1}^{m} - \frac{1}{α} - \frac{1}{α^{2}} \log (- \log (u_{k})) \\ = & - \frac{m}{α} - \frac{1}{α^{2}} \sum_{k = 1}^{m} \log (- \log (u_{k})) \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \log \left( -\phi ^{\prime }\left( u_{k}\right) \right) & =& \log \left( \frac{1}{\alpha }\left( -\log u_{k}\right) ^{\frac{1}{\alpha }-1}\frac{1}{u_{k}}\right) \\ & =& -\log \alpha -\log \left( u_{k}\right) +\left( \frac{1}{\alpha }-1\right) \log \left( -\log \left( u_{k}\right) \right) \\ \frac{d\sum _{k}\log \left( -\phi ^{\prime }\left( u_{k}\right) \right) }{d\alpha } & =& \sum _{k=1}^{m}-\frac{1}{\alpha }-\frac{1}{\alpha ^{2}}\log \left( -\log \left( u_{k}\right) \right) \\ & =& -\frac{m}{\alpha }-\frac{1}{\alpha ^{2}}\sum _{k=1}^{m}\log \left( -\log \left( u_{k}\right) \right) \end{eqnarray*}