calculus and analysis – Slow Derivative with Sum and Subscripts

I am writing a function that takes derivatives of functions involving subscripts and an open-ended Sum. It’s unreasonably slow. A minimal example (the real situation is much worse):

D(Sum(Exp(-(xx - Subscript(x, j))^2/(V + Subscript(Vx, j)^2)) Subscript(n, j), {j, nsp}), xx) // AbsoluteTiming

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If I get rid of the Subscript it gets better:

D(Sum(Exp(-(xx - x(j))^2/(V + Vx(j)^2)) n(j), {j, nsp}), xx) // AbsoluteTiming

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but the Sum is also contributing to the slowness. Focusing on the summand is much faster, with or without subscripts:

D(Exp(-(xx - Subscript(x, j))^2/(V + Subscript(Vx, j)^2)) Subscript(n, j), xx) // AbsoluteTiming

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D(Exp(-(xx - x(j))^2/(V + Vx(j)^2)) n(j), xx) // AbsoluteTiming

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Any ideas on how I get speed up this sort of operation? Not using subscripts is kind of off the table.