Yes, using chain rule for the gradient of norm(Ax-b)^2 makes that derivation a lot shorter. Or just citing a theorem for the gradient of the L2 norm would have

Yes, using chain rule for the gradient of norm(Ax-b)^2 makes that derivation a lot shorter. Or just citing a theorem for the gradient of the L2 norm would have been fine. I used the FOIL approach because each of the 4 terms can be tackled using very elementary theorems in matrix calculus - a constant term, two linear terms, and a quadratic form. But in retrospect this was probably a mistake seeing as several people have gotten hung up on it.