Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 2 / 8E / e

Let $f$ and $g$ be conserved quantities, allowing explicit time dependence. ThenUsing bilinearity of the Poisson bracket, commutation of partial differentiation with it, and the Jacobi identity for the Poisson bracket,Thus $\{f,g\}$ is also conserved.