Topic: The Derivative from First Principles

Quadratic Derivatives by Factoring

Polynomial Derivatives at an Arbitrary Point

Pointwise Differentiability Versus Differentiability on an Interval

Piecewise Linear Functions at a Join

Oscillation in a Difference Quotient

One-Sided Difference Quotient Limits

Discontinuity as a Test for Nondifferentiability

Differentiating Piecewise Formulas Away from Their Joins

Difference Quotients for Cube Roots Away from Zero

Deriving Linearity Directly from the Difference Quotient