= Solution
The <Poisson bracket> in canonical coordinates is
$$
\boxed{\{f,g\}=\sum_i\left(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial f}{\partial p_i}\frac{\partial g}{\partial q_i}\right).}
$$
Using <Hamilton's equations> $\dot q_i=H_{p_i}$ and $\dot p_i=-H_{q_i}$ in the <chain rule> yields
$$
\boxed{\frac{df}{dt}=\frac{\partial f}{\partial t}+\{f,H\}.}
$$
The partial time derivative holds phase-space coordinates fixed; the total derivative follows the actual trajectory.
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