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

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(, = 0,