Why does derivative of sum(u) result in vector of 1s?

Question

I came across these formulas (please see attached) in a paper. Could you please explain why the derivative of sum(u) where u is the dot product of vectors w and x results in vector of 1s? Thanks derivative of sum of dot product between two vectors

Answer 1

The sum() function itself is a dot product, i.e. $$y = {\rm sum}(u) = 1^Tu$$ Therefore its differential and derivative are $$dy = 1^Tdu \quad\implies\quad\frac{\partial y}{\partial u} = 1^T$$