Differentiation
A 18-module path through differentiation, in study order from foundations to the frontier.
Modules
- The Derivative: Definition via Difference Quotients
- Differentiability Implies Continuity
- Algebraic Rules of Differentiation
- The Chain Rule
- Interior Extrema and the Vanishing Derivative
- Rolle's Theorem
- The Mean Value Theorem
- The Cauchy Mean Value Theorem
- Monotonicity and the Sign of the Derivative
- Zero Derivative Implies Constant
- Darboux's Theorem: The Intermediate Value Property of Derivatives
- L'Hopital's Rule
- Higher-Order Derivatives
- Taylor's Theorem with Remainder
- Lagrange and Cauchy Forms of the Remainder
- Taylor Polynomials and Local Approximation
- Convexity and the Second Derivative
- Derivatives of Inverse Functions