Looks like something went wrong with your cut-and-paste:
>Let us think of x as a quantity that can grow by a small amount so as to become x+dx, where dx is the small increment added by growth. The square of this is x²+2x⋅dx+(dx)². The second term is not negligible because it is a first-order quantity; while the third term is of the second order of smallness, being a bit of, a bit of x².
I always enjoyed calculus, I thought it was kind of magical and didn't worry too much about where the magic came from. I've known the derivative of x^2 is 2x for nearly 50 years but just found out why due to your formatting correction here. Thanks! Also gratitude for the poster who explained that the fundamental theorem of calculus (i.e. reverse differentiation is integration) is essentially just the calculation involved in going from an odometer reading to a speedometer reading then back again!
>Let us think of x as a quantity that can grow by a small amount so as to become x+dx, where dx is the small increment added by growth. The square of this is x²+2x⋅dx+(dx)². The second term is not negligible because it is a first-order quantity; while the third term is of the second order of smallness, being a bit of, a bit of x².