Differentiation

Differentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables.

In simple terms, it is a way of finding how things change. Imagine you're driving a car and looking at how your speed changes over time. If you want to know how fast your speed is increasing or decreasing, that's differentiation in action.

Key Concepts in Differentiation

This section covers key differentiation concepts, rules, and applications, including the Mean Value Theorem, derivative techniques, and real-life uses of derivatives.

• Differentiability
  • Mean Value Theorem: Cauchy's Mean Value Theorem
  • Rolle's Mean Value Theorem
• Derivative
  • Derivative by First Principle
  • Algebra of Derivative of Functions
• Rules for Differentiation
  • Power Rule
  • Product Rule
  • Quotient Rule
  • Chain rule
• Formulas for Differentiation
  • Implicit Differentiation
  • Logarithmic Differentiation
  • Parametric Differentiation
• Examples of Derivatives
  • Derivatives of Polynomial Functions
  • Derivatives of Trigonometric Functions
  • Derivatives of Exponential Functions
  • Derivatives of Logarithmic Functions
  • Derivatives of Inverse Trigonometric Functions
  • Derivatives of Inverse Functions
  • Derivatives of Composite Functions
• Application of Derivatives
  • Critical Points
  • Rate Change of Quantities
  • Increasing Function
  • Decreasing Function
  • Approximation
  • Maxima or Minima: Absolute Minima and Maxima | Relative Minima and Maxima
  • Tangent and Normal
• Concavity and Points of Inflection
• Curve Sketching
• Partial Derivatives
• Higher Order Derivatives
• Real-Life Application of Differentiation

Practice on Differentiation

This section provides practice quizzes and problems to help reinforce your understanding of differentiation, including its applications and partial derivatives.

• Differentiation - Quiz
• Application of Differentiation - Practice Questions
• Partial Derivatives Practice Problems

Differentiation for Programmers

This section focuses on differentiating polynomials and derivatives using programming, with examples in MATLAB to help you implement differentiation techniques in code.

• Program to Differentiate the Given Polynomial
• Program for Derivative of a Polynomial
• Differential or Derivatives in MATLAB
• MATLAB – Differentiation