Finding the equation of motion for Born-Infeld lagrangian

[vahdaneh]

Homework Statement

finding equation of motion for Born-Infeld lagrangian

Relevant Equations

born-infelf lagrangian

Homework Statement: finding equation of motion for Born-Infeld lagrangian
Homework Equations: born-infelf lagrangian

i do not know where I'm going wrong.
i'll be really grateful for any advice.

 

[member 553083]

The Born-Infeld Lagrangian for a scalar field $\phi$ is given as$$L=\sqrt{1+\partial_\mu\phi\partial^\mu\phi}-V(\phi)$$where $V(\phi)$ is the potential of the scalar field.The equation of motion can be obtained by taking the Euler-Lagrange equation $$\frac{\partial L}{\partial \phi} - \partial_\mu \left(\frac{\partial L}{\partial (\partial_\mu \phi)}\right)=0.$$Using this equation, the equation of motion for $\phi$ is$$\partial_\mu\left(\frac{\partial_\mu\phi}{\sqrt{1+\partial_\nu \phi \partial^\nu \phi}}\right) - \frac{dV}{d\phi}=0.$$