Public learning track
Limits, First Principles, and Derivative Foundations
12th Grade · Math · Open Global Math
7 lessons
Goal
Understand derivatives as limits of difference quotients, differentiate fundamental functions from first principles, and interpret first and second derivatives geometrically.
Featured Diagrams
Limits and the Definition of the Derivative
7 lessons
0 of 7 done
- 1Limits and the Definition of the DerivativeUp nextStart
- 2Differentiating Linear and Quadratic Functions from First PrinciplesPremiumNot started yet
- 3Differentiating Cubic and General Integer Powers from First PrinciplesNot started yet
- 4Differentiating Sine and Cosine from First PrinciplesNot started yet
- 5Geometric Interpretation of the First Derivative as Tangent SlopeNot started yet
- 6Second Derivatives, Concavity, and Points of InflectionNot started yet
- 7Higher-Order Derivatives and Kinematic InterpretationsNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
7 lessons
Limits, First Principles, and Derivative Foundations
Understand derivatives as limits of difference quotients, differentiate fundamental functions from first principles, and interpret first and second derivatives geometrically.
2
11 lessons
Differentiation Rules and Transcendental Functions
Differentiate power, exponential, logarithmic, and trigonometric functions using product, quotient, chain, and inverse differentiation rules.
3
7 lessons
Implicit Differentiation, Parametric Curves, and Related Rates
Differentiate implicit relations and parametric equations, and solve connected rates of change problems.
4
7 lessons
Applications of Derivatives: Extrema and Optimization
Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.
5
8 lessons
Definite Integrals and the Fundamental Theorem of Calculus
Understand integration as the limit of Riemann sums, apply the Fundamental Theorem of Calculus, and integrate standard function families.
6
8 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Master advanced integration methods including u-substitution, integration by parts, and partial fractions for definite and indefinite integrals.
7
6 lessons
Area Under Curves and Between Intersecting Functions
Evaluate definite integrals to calculate the total geometric area under a curve and enclosed between intersecting curves.
8
9 lessons
Differential Equations and Mathematical Modeling
Formulate first-order differential equations from contextual scenarios, find general and particular solutions via separation of variables, and analyze model behavior.