The Euler-Lagrange Equation is a fundamental equation in the field of calculus of variations, which helps find the path or function that minimizes or maximizes a certain quantity. It is derived from the principle of least action, stating that the actual path taken by a system is the one for which the action integral is stationary (usually a minimum). In mathematical terms, the equation relates the derivative of a function to its variations, providing a systematic way to derive equations of motion in physics. It is widely used in various fields, including classical mechanics, quantum mechanics, and economics, to solve optimization problems involving functions.