thanks for the quick reply!
Let’s say a = (a1, a2, a3)
then y = (y1, y2, y3) = (a1, a2, a3) / (a1 + a2 + a3).
then d(y1) / d(a1) = (a2 + a3) / (a1 + a2 + a3) ^ 2
and similarly, d(y2) / d(a2) = (a1 + a3) / (a1 + a2 + a3) ^ 2
So they should be different rather than same?