Public learning track
First Principles and Foundations of Derivatives
11th Grade · Math · Open Global Math
7 lessons
Goal
Derive the derivative definition from difference quotients, prove standard derivatives from first principles, and analyze second derivatives and curvature.
Featured Diagrams
The Derivative Function and Differentiability from First Principles
7 lessons
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- 1The Derivative Function and Differentiability from First PrinciplesUp 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 Functions from First PrinciplesNot started yet
- 5Second Derivatives, Concavity, and Points of InflectionNot started yet
- 6The Second Derivative Test for Local ExtremaNot started yet
- 7Points of Inflection and Non-Zero Gradient InflectionsNot started yet
Standards Covered
- OGM.12.CAL.1Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Understand the derivative f'(x) as the limit of the difference quotient and as the gradient of the tangent; differentiate x^n, sin(x), cos(x) from first principles; compute second derivatives to determine convexity, concavity, and points of inflection.
- OGM.12.CAL.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Apply differentiation to find equations of tangents and normals, identify intervals of increase/decrease, locate and classify stationary points (local/global extrema, points of inflection), and differentiate implicitly and parametrically.
Curriculum Framework
11th Grade · Math · Open Global Math
1
7 lessons
First Principles and Foundations of Derivatives
Derive the derivative definition from difference quotients, prove standard derivatives from first principles, and analyze second derivatives and curvature.
2
11 lessons
Advanced Differentiation Rules and Transcendental Functions
Differentiate exponential, logarithmic, and trigonometric functions using chain, product, and quotient rules.
3
7 lessons
Implicit and Parametric Differentiation and Rates of Change
Differentiate implicit equations and parametric curves, and solve connected rates of change modeling problems.
4
8 lessons
Applications of Derivatives: Tangents, Extrema, and Curve Sketching
Construct tangent and normal lines, classify local and global extrema, and sketch complex transcendental curves.
5
8 lessons
Definite Integrals, Riemann Sums, and the Fundamental Theorem of Calculus
Interpret definite integrals as limits of Riemann sums, apply the Fundamental Theorem of Calculus, and calculate areas under and between curves.
6
9 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Evaluate non-standard integrals using algebraic substitution, integration by parts, and partial fraction decompositions.
7
6 lessons
First-Order Differential Equations and Modeling
Formulate, solve, and interpret separable first-order differential equations in physical, biological, and kinematic contexts.
8
7 lessons
Numerical Calculus and Iterative Methods
Locate roots via sign change, solve equations using fixed-point iteration and Newton-Raphson, and approximate integrals with the trapezium rule.