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May 9, 2022 at 10:24 comment added Alexei Boulbitch I do not understand what you mean under "only one summation sign whose index is i+j". Indeed, the polynomial in your comment is written exactly like you will obtain opening the expression that I have given in the answer.
May 8, 2022 at 12:11 comment added VH84 Many Thanks, @Alexei Boulbitch! I think you got the "spirit", however, this is not exactly what is asked. Let me explain it better. I want to obtain the first and second derivatives of the following polynomial: $\sum^{N}_{i+j=0}\alpha_{ij}x^{i}y^{i} \equiv \alpha_{00}+\alpha_{10}x+\alpha_{01}y+a_{11}xy+\ldots+a_{0n}y^{n}$. As you may see, the polynomial posses only one summation sign whose index is $i+j$$. I will update my post and include my attempts. Thanks once more for your help.
May 8, 2022 at 11:34 history answered Alexei Boulbitch CC BY-SA 4.0