The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force

$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}) \qquad(1),$$

and the corresponding Lagrangian is

$$L = \dfrac{1}{2}mv^2 - q\phi(\textbf{r},t)+q\textbf{v} \cdot \textbf{A} \qquad(2).$$

My question is: How to derive the equation $(1)$ just from $(2)$ ?

The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force

$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$

and the corresponding Lagrangian is

$$L = \dfrac{1}{2}mv^2 - q\phi(\textbf{r},t)+q\textbf{v} \cdot \textbf{A}. \tag{2}$$

My question is: How to derive the equation $(1)$ just from $(2)$ ?