This is a good point. Noting that "d/dx" is a vector (field) is an antidote to the ideas that vectors are little arrows, or "a magnitude and a direction", or an

This is a good point. Noting that "d/dx" is a vector (field) is an antidote to the ideas that vectors are little arrows, or "a magnitude and a direction", or an ordered list with numbers in the slots. Vectors can be thought of in lots of ways, and here they're thought of as operators on functions.