Multivariable Function Differentiation
Overview
Jacobian Matrix
Given a vector function {% \vec{F} (x_1, ... ,x_n) %}, where the dimension of {% \vec{F} %} is m, then
the differential of {% \vec{F} %} is
{%
d\vec{F} = (\frac{\partial \vec{F}}{\partial x_1}, ... ,\frac{\partial \vec{F}}{\partial x_n} )
=\begin{bmatrix}
\frac{\partial{F_1}}{\partial{x_1}} & ... & \frac{\partial{F_1}}{\partial{x_n}} \\
& ... & \\
\frac{\partial{F_m}}{\partial{x_1}} & ... & \frac{\partial{F_m}}{\partial{x_n}} \\
\end{bmatrix}
%}
