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Derivative, Sum and KroneckerDelta symbolically


Hi,

does anybody know how to tell Mathematica to solve  

"Sum[D[Sum[x[n], {n, 1, k}], x[i]], {i, 1, k}]" correctly? 

In my opinion the expression should give "k" as result, Mathematica says
"0".
Introducing concrete values instead of k the result is correct:

"Sum[D[Sum[x[n], {n, 1, 5}], x[i]], {i, 1, 5}]" = "5".

Is there a possibility to tell Mathematica that the expressions above
lead to a "KroneckerDelta": 

Sum[KroneckerDelta[n, i], {n, 1, k}, {i, 1, k}] 


Thanks,

Stefan


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