Prove `F = - (dV)/(dx)` for conservative force .

Explanation

Suppose that a body undergoes displacement `Deltax` under the action of a conservative force F .
` :. ` Work done by this force ,
`W = F Delta`
but according to work energy theorem ,
`W = DeltaK `
` :. DeltaK = F Deltax`
Now from the law of conservation of mechanical energy .
`DeltaK + DeltaV = 0 `
` :. F DeltaX + DeltaV = 0 `
` :. F Deltax + DeltaV = 0 `
` :. F = DeltaV `
`Deltax`
Hence , in the case of conservative force , force will be obtained by taking negative derivative of potential energy w.r.t to displacement .