Partial Derivative - Pattern Recognition Bishop section 2.3
$$\frac{\partial}{\partial \mu} (x_n^Tx_n)=0, $$$$\frac{\partial}{\partial \mu}( -\mu^Tx_n)=-x_n$$
$$\frac{\partial }{\partial \mu}(\mu^T\mu) = 2\mu$$
Note that if $A$ is symmetric, then $$\frac{\partial }{\partial y}(y^TAy)=2Ay.$$


\begin{align}\frac{\partial }{\partial \mu}\left(-\frac12 (x_n-\mu)^T\Sigma^{-1}(x_n-\mu) \right)&amp;=-\frac12\frac{\partial }{\partial \mu}\left( (\mu-x_n)^T\Sigma^{-1}(\mu-x_n) \right)\\
&amp;=-\frac12\left(2\Sigma^{-1}(\mu-x_n) \right)\\
&amp;= \Sigma^{-1}(x_n-\mu)\end{align}