matrix multiplication markdown

$$
\mathbf{J}
=
\frac{d \mathbf{f}}{d \mathbf{x}}
=
\left[ \frac{\partial \mathbf{f}}{\partial x_1}
\cdots \frac{\partial \mathbf{f}}{\partial x_n} \right]
=
\begin{bmatrix}
\frac{\partial f_1}{\partial x_1} & \cdots &
\frac{\partial f_1}{\partial x_n} \\
\vdots & \ddots & \vdots \\
\frac{\partial f_m}{\partial x_1} & \cdots &
\frac{\partial f_m}{\partial x_n}
\end{bmatrix}
$$

$$f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}$$