Alternative Equation Formats

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MathML

\frac{\partial l_{n}}{\partial θ_{i}} = \frac{0.5 (d f + m)}{(1 + q^{'} Σ^{- 1} q / d f)} [\frac{(2 q^{'} Σ^{- 1} \frac{\partial q}{\partial θ_{i}})}{d f} + q^{'} Σ^{- 1} \frac{\partial Σ}{\partial θ_{i}} Σ^{- 1} q] - \frac{n}{2} t r a c e (Σ^{- 1} \frac{\partial Σ}{\partial θ_{i}})

MathML rendered with MathJax

\frac{\partial l_{n}}{\partial θ_{i}} = \frac{0.5 (d f + m)}{(1 + q^{'} Σ^{- 1} q / d f)} [\frac{(2 q^{'} Σ^{- 1} \frac{\partial q}{\partial θ_{i}})}{d f} + q^{'} Σ^{- 1} \frac{\partial Σ}{\partial θ_{i}} Σ^{- 1} q] - \frac{n}{2} t r a c e (Σ^{- 1} \frac{\partial Σ}{\partial θ_{i}})

Math as LaTeX Source

\[ \frac{\partial l_ n}{\partial \theta _ i} = \frac{0.5 (df + m)}{(1 +\mb{q} '\bSigma ^{-1} \mb{q} /df)} \left[\frac{(2 ~ \mb{q} '\bSigma ^{-1} \frac{\partial \mb{q} }{\partial \theta _ i} )}{df} + \mb{q} ' \bSigma ^{-1} \frac{\partial \bSigma }{\partial \theta _ i} \bSigma ^{-1} \mb{q} \right] - \frac{n}{2} \mr{trace} ( \bSigma ^{-1} \frac{\partial \bSigma }{\partial \theta _ i}) \]