# Derivative over double summation?

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SAMUEL AYINDE on 12 Jan 2019
Commented: Walter Roberson on 14 Jan 2019
Please, can someone help me find the derivatives in this attachment? You can solve it in the attached excel document or solve it in word document and post the snap shot of the solution. Thank you so much.
David Goodmanson on 13 Jan 2019
Hi Samuel,
so by dP/dm do you mean a matrix whose ij component is dP/dm_ij?
Also the summand in each of the double sums defining P is identical, so the two double sums are almost identical, differing only in slight chages in the upper limits. Is this what is intended?
SAMUEL AYINDE on 13 Jan 2019
Yes, dP/dm is a matrix whose ij component is dP/dm_ij. Yes, the double sums are almost identical. They differ only slightly in the upper limits. That exactly is what is intended.

Walter Roberson on 13 Jan 2019
The derivative of absolute value is not well defined.
SAMUEL AYINDE on 14 Jan 2019
Edited: SAMUEL AYINDE on 14 Jan 2019
Hi Walter,
I can go with your approximation of absolute value. Now, I want to find dP/dm_ij in the equation below. Can you please help me? Thank you so much.
Walter Roberson on 14 Jan 2019
The solution is as I gave before with the difference of sign() , but remember you need to be careful on the boundary condition .
The derivative is 0 except for at most two terms because the m variable are independent except the two cases of identical subscripts. So you can break it down to three cases, one for each of the two boundary conditions and one for the centre. You can then vectorize for the centre and vectorize for each of the two boundary conditions . or perhaps it works out to be four boundary conditions . Small number of them anyhow .

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