Part 2

differentiation

• 2.1

  The derivative as a limit

  A slope needs two points, and a tangent line only has one. The difference quotient is how you get the second one and then take it away again.

  7 min
• 2.2

  The differentiation rules

  Power, product, quotient. Each is a shortcut for a limit you would otherwise compute by hand, and each has a failure mode worth naming.

  4 min
• 2.3

  The chain rule

  The rule for a function inside a function, and the one students most often apply without noticing they needed to.

  5 min