Bridging connection between Newton’s second law and Work

1. The problem statement, all variables and given/known data

I’m trying to bridge F =ma to m/2(dv2/dx). It was shown in the course book I have but there’s a huge disconnection in the steps.

3. The attempt at a solution

F =ma = m.(dv/dt) = m(dv/dx . dx/dt) = mv(dv/dx). Where do I take it from here?

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