Differentiation

The derivative is a number attached to a function at a point, when that number exists. This chapter gets the definition from secants, then the algebra that lets me stop expanding ${(𝑎+h)}^{𝑛}$ by hand, then the chain rule that walks a composite backwards.

I am not starting from “the slope of the tangent.” I will earn that picture from the difference quotient. Continuity will show up as something the derivative implies and does not follow from.