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## Main Question or Discussion Point

In Lagrangian mechanics, the Euler-Lagrange equations take the form $$\frac{\partial L}{\partial x} = \frac{\mathbb{d}}{\mathbb{d}t}\frac{\partial L}{\partial \dot{x}}$$ From this, we can define the left side of the equation as force, and by carrying out the actual derivative, we get $$F = -\frac{\partial V}{\partial x}$$ But by definition, this is only true for conservative forces; in other words, there exist forces that cannot be expressed in this form, such as friction or drag. So are these forces simply inexpressible in Lagrangian mechanics without recourse to the Newtonian formulation, or is there simply something I'm not seeing?