In the latter case, it is assumed that all the elements of the array depend on all the variables in the succeeding varlist. DIFF differentiates exp with respect to each vi, ni times. No further simplification of DEL is offered. Then all the derivative indices will be sorted. The result uses the noun form of any derivatives arising from expansion of the vector differential operators.
Unevaluable items come out quoted.
If fewer than n gradients, say i, are given, then they refer to the first i arguments of f. The xi are merely dummy variables as in function definition headers and are used to indicate the ith argument of f. Gradients are needed when, for example, a function is not known explicitly but its first derivatives are and it is desired to obtain higher order derivatives. These may be supplied either before or after the transform is taken. Since the initial conditions must be specified at zero, if one has boundary conditions imposed elsewhere he can impose these on the general solution and eliminate the constants by solving the general solution for them and substituting their values back.