Much discussion of backprop could be avoided by recalling that the bit that does the work is the chain rule from calculus. Error terms represent a sum and prod

Much discussion of backprop could be avoided by recalling that the bit that does the work is the chain rule from calculus. Error terms represent a sum and product of derivatives. The product of a bunch of terms will tend to get really big or really small. The rest is detail: are the terms in some interval? Which? how many are we multiplying? how many are we summing over? do we doctor the sum after we get it?