Is there a generic form of that for any nth derivative?

Sum over integers k from 1 to n of A(k)*e^(e^(2*i*pi/k)*x) is its own nth derivative, for all A.

Is there a generic form of that for any nth derivative?

Sum over integers k from 1 to n of A(k)*e^(e^(2*i*pi/k)*x) is its own nth derivative, for all A.