Note to moderator: Read the answerline carefully. For the Lax pair L-comma-M, [read slowly] this operation of an eigenfunction of L, plus “M times the eigenfunction,” equals another eigenfunction. This operation of the generating function is the difference between the final and initial Hamiltonians. This operation of the principal function is the negative of the Hamiltonian. This operation of the distribution function equals the negative of “the Poisson (“pwah-SAWN”) bracket of the distribution function and the Hamiltonian,” as follows from Liouville’s (“lyoo-VEEL’s”) theorem. If this operation of the Lagrangian is zero, energy is conserved. Adding terms of the form “q-dot times delta-by-delta-q” to this operation yields a “total” operation. For 10 points, name this operation that, while holding all other variables constant, gives the rate of change of a function with respect to a quantity measured in seconds. ■END■
ANSWER: partial time derivative [or partial derivative with respect to time; or partial differentiation with respect to time; or partially differentiating with respect to time; accept t in place of “time”; accept delta by delta t; accept delta sub t; accept any answer preceded by “negative” or “minus” or equivalents; prompt on (first) time derivative, (first) derivative with respect to time, differentiation with respect to time, differentiating with respect to time, d by dt, or negative equivalents; reject “total time derivative” or “total derivative with respect to time]
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= Average correct buzz position