Anyone know how to interpret the euler-lagrange differential equation?

[Gardenharvest]

Hi,
I am having a calculus class now and these days the instructor is introducing the Euler-Lagrange differential equation. I have no idea why the formula (general form) is like that way. Is anyone here know how to interprete the formula and help me to understand it?

dF/df-(d/dx)dF/df'=0

Many thanks.

 

[Pengwuino]

The way it's introduced in physics is how it satisfies least-action principles using variational calculus; that is the variation of the action is 0: $$\[ \delta \int {L(\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over x} } ,\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over x} ',t)dt = 0 \]$$

The Euler-Lagrange equations determine your equations of motion.