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\[ \begin{split} \frac{\partial{\mathcal{E}}}{\partial{x_l}} & = \frac{\partial{\mathcal{E}}}{\partial{x_L}}\frac{\partial{x_L}}{\partial{x_l}}\\\\ & = \frac{\partial{\mathcal{E}}}{\partial{x_L}}\Big(1+\frac{\partial{}}{\partial{x_l}}\sum_{i=l}^{L-1} \mathcal{F}(x_i,\mathcal{W}_i)\Big) \end{split} \]

\[ P(A_i \mid B) = \frac{P(B\mid A)P(A_i)}{\sum_{j=1}^{n}P(A_j)P(B \mid A_j)} \]

\[\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 5 & 5 & 5 \\ 5 & 5 & 5 & 5 \\ 5 & 5 & 5 & 5 \\ 5 & 5 & 5 & 5 \end{bmatrix}\]

\[\begin{equation} \textstyle \prod_{i=1}^N x_i \end{equation}\]

\[\begin{equation} \textstyle \coprod_{i=1}^N x_i \end{equation}\]

\[\begin{equation} \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx \end{equation}\]

\[\begin{equation} \iiint\limits_E dx\,dy\,dz \end{equation}\]

\[\begin{equation} \bigcap_{i=1}^n E_i \end{equation}\]

\[\begin{equation} \binom{n}{k} \end{equation}\]

\[\begin{vmatrix} x & y \\ z & v \end{vmatrix}\] \[\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}\] \[\begin{array}{ | c | c | c | } a & b & S \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\]

\[\begin{equation} f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} \end{equation}\]

\[\begin{equation} \lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rfloor \biggr\rfloor \Bigr\rfloor \bigr\rfloor \rfloor \end{equation}\]

\[\begin{equation} \left\{ \begin{array}{lr} x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\ y=s, & 0 \leq s \leq L,|t| \leq1. \\ z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), & \end{array} \right. \end{equation}\]