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

1.	Prove F = - (dV)/(dx) for conservative force .
Answer» Solution :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 .

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