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Question for Partial differential summationseries


The function defined as follow


x = X[t];
y = Y[i, t];
p = P[i, xv];
w = Sum[y*p, {i, 1, N}];

When we excuted partial differential "w" by "y"
the exact solution is "p" (or P[i, xv]).

However, the solution in Mathematica package is 
Sum[p, {i, 1, N}].

How can I obtain the correct solution? please help.



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