The Euler-Lagrange equation (16.14) is used in a field theory context in this chapter, but it is applicable to a broad range of problems. Show that inserting a Lagrangian \(L(x, \dot{x})=\frac{1}{2} \dot{m}^{2}-V(x)\) in Eq. (16.14) leads to Newton's second law of motion.

Data from Eq. 16.14

(, = 0,