Mathematics chapters
  1. 013D Geometry
  2. 02Application of Derivatives
  3. 03Area Under Curves
  4. 04Binomial Theorem
  5. 05Circles
  6. 06Complex Numbers
  7. 07Continuity & Differentiability
  8. 08Definite Integration
  9. 09Determinants
  10. 10Differential Equations
  11. 11Ellipse
  12. 12Hyperbola
  13. 13Indefinite Integration
  14. 14Inequalities & Modulus
  15. 15Inverse Trigonometric Functions
  16. 16Limits
  17. 17Logarithms
  18. 18Matrices
  19. 19Methods of Differentiation
  20. 20Number System & Basics
  21. 21Parabola
  22. 22Permutations & Combinations
  23. 23Probability
  24. 24Properties of Triangle
  25. 25Quadratic Equations
  26. 26Sequences & Series
  27. 27Sets, Relations & Functions
  28. 28Statistics
  29. 29Straight Lines
  30. 30Trigonometric Equations
  31. 31Trigonometric Ratios & Identities
  32. 32Vectors

Chapter 19 · Class 11-12 & JEE Main/Adv

Methods of Differentiation

19 topics in 4 parts

Full lessonClass 12 Mathematics · Differential Equations
Derivative from First Principles Constant Rule Power Rule Constant Multiple and Sum Rules Product Rule Quotient Rule

Key ideas

+Y +Z +X O(0,0,0) Line L A(x₁, y₁, z₁) a P(x, y, z) r Parallel Vector b = aî + bĵ + ck̂ Cartesian Form: (x - x₁)/a = (y - y₁)/b = (z - z₁)/c = λ ⟺ General Point: (x₁ + λa, y₁ + λb, z₁ + λc)
Methods of Differentiation

Analytical Comparison & Distinction Matrix

Analytical MethodStandard RepresentationParametric / Invariant Framework
Algebraic NatureExplicit equations relating spatial coordinatesParameterized using scalar parameters (λ, μ) or vectors
Symmetry UsageRelies on coordinate expansionExploits vector dot/cross products for rapid simplification
Computational EfficiencyDirect for intercept evaluationSuperior for angles, orthogonal projections, and distances
Common MistakeSign confusion in determinantsOmitting boundary condition checks

All 19 topics in Methods of Differentiation

  1. Methods of Differentiation

    • Derivative of Some Standard Functions
    • Basic Differentiation Rules
    • Differentiation of Functions in Parametric Form
    • Differentiation Using Logarithms
    • Differentiation of Determinants
    • Differentiation of Implicit Functions
    • Differentiation of Inverse Functions
    • Differentiation of Inverse Trigonometric Functions
    • Differentiation of One Function With Respect to Another
    • Differentiation of Functional Equations
    • Differentiation of Piecewise & Modulus Functions
    • Geometrical Meaning of a Derivative
    • Higher Order Derivatives
    • Theorems on Derivatives

  2. Errors & Approximations

    • Errors & Approximations

  3. Rate Measure

    • Rate Measure

  4. Methods of Differentiation

    • Differentiation of Trigonometric Function
    • Differentiation of Composite Function
    • Chain Rule