Derivative Matrix

For a given function $f:{\mathbb{R}}^n\to {\mathbb{R}}^k$ The derivative $Df(x_0)$ is the matrix:

$$Df=\left[\frac{\partial f_i}{\partial x_j}\right]=\left[\begin{array}{ccc}\frac{\partial f_1}{\partial x_1}& \dots & \frac{\partial f_1}{\partial x_n}\\ ⋮& \dots & ⋮\\ \frac{\partial f_k}{\partial x_1}& \dots & \frac{\partial f_k}{\partial x_n}\end{array}\right]$$