Alternative Equation Formats

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MathML

\begin{aligned} g (β_{j}) & = \frac{\partial S S E (β)}{\partial β_{j}} = - 2 \sum_{i = 1}^{n} (y_{i} - f_{i} (β)) \frac{\partial f_{i} (β)}{\partial β_{j}} \\ {[H (β)]}_{j k} & = \frac{\partial S S E (β)}{\partial β_{j} \partial β_{k}} = 2 \sum_{i = 1}^{n} \frac{\partial f_{i} (β)}{\partial β_{j}} \frac{\partial f_{i} (β)}{\partial β_{k}} - (y_{i} - f_{i} (β)) \frac{\partial^{2} f_{i} (β)}{\partial β_{j} \partial β_{k}} \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \mb{g}(\beta _ j) & = \frac{\partial \mr{SSE}(\bbeta )}{\partial \beta _ j} = -2 \sum _{i=1}^{n} \left(y_ i - f_ i(\bbeta )\right) \frac{\partial f_ i(\bbeta )}{\partial \beta _ j} \\ \left[\mb{H}(\bbeta )\right]_{jk} & = \frac{\partial \mr{SSE}(\bbeta )}{\partial \beta _ j \partial \beta _ k} = 2 \sum _{i=1}^{n} \frac{\partial f_ i(\bbeta )}{\partial \beta _ j} \frac{\partial f_ i(\bbeta )}{\partial \beta _ k} - \left(y_ i - f_ i(\bbeta )\right) \frac{\partial ^2 f_ i(\bbeta )}{\partial \beta _ j\partial \beta _ k} \\ \end{align*}