I believe you're correct. (I haven't thought through the full context, but that shouldn't be necessary for that equation... I hope.) I've edited it. Thanks!
Partial, I think. I mean, it's all with respect to one variable.
(Looking at this post now, it really should have included concrete numbers in addition to the symbols, which would also have answered the question. Idk if I'll get around to fixing it...)
Just another quick question about this part: The first term is ∂ℓ∂z9=∂(y−z9)2∂z9=2z9.
Shouldn't this be: ∂(y−z9)2∂z9=−2(y−z9)?
You mentioned just after something about notation, but I wanted to understand a bit better in case I'm missing something