Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / Section B / B7 / ii / Solution

The work-energy theorem gives $dK={\mathbf{F}}_{\mathrm{net}}\cdot d\mathbf{r}$ for a point particle. For a conservative force, $\mathbf{F}=-\nabla U$ and its work is $-\Delta U$. Force is not generally a scalar derivative of total energy without specifying the displacement and the relevant energy.