I have gotten several emails over the years from angry mathematicians, saying or implying that my mentioning this derivation is some sort of strawman. They tell me they don't prove the derivative that way and then launch into some longwinded torture of both mediums (math and the English language) to show me how to do it. Unfortunately, this derivation above is much more than a strawman. It is the way I was taught the calculus in high school in the early 80's, and it is posted all over the internet to this day. If it is a strawman, it is the mainstream's own strawman, and they had best stop propping it up. These mathematicians are just angry I am using their own equations against them.