I think that one of the reasons people look for a good exposition is so that they do not _have_ to muddle through. I know I look for a simple example or explan

I think that one of the reasons people look for a good exposition is so that they do not _have_ to muddle through. I know I look for a simple example or explanation that makes complicated cases clear. This 'explanation' might be correct, but I found the details that would help someone else follow it are missing. Especially someone with a computer science background who considers a m x 1 matrix different from a 1 x m matrix. I see a sister comment has explained this, but I want to point out that there are plenty of details... (like sister's statement 0b which looks to me more like an exponential function than a linear function) that's why one goes to a carefully written source. This paper is a carefully written explanation of the basics, ending with many applications of the chain rule. The "matrix product rule" is not mentioned, which is good in my opinion.