Total Differentials and Time Derivatives

In both classical mechanics and quantum mechanics one often has to deal with total time derivatives of functions depending on many time-dependent arguments. For example, consider a real-valued function / depending on N time-dependent arguments Xi t) and explicitly on the time t itself, 

The partial time derivative of the function / is simply given by 

This rule has, for example, been extensively applied in the discussion of Hamiltonian mechanics in section 2.3. By formal multiplication of Eq. (A.32) by df the total differential of the function / is recovered. 

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