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.
This section covers key differentiation concepts, rules, and applications, including the Mean Value Theorem, derivative techniques, and real-life uses of derivatives.
- Differentiability
- Derivative
- Derivative by First Principle
- Algebra of Derivative of Functions
This section introduces the fundamental rules and methods used to compute derivatives of different types of functions efficiently.
- Rules for Differentiation
- Power Rule
- Product Rule
- Quotient Rule
- Chain rule
- Formulas for Differentiation
- Implicit Differentiation
- Logarithmic Differentiation
- Parametric Differentiation
Here, you’ll find derivatives of commonly used functions, which form the building blocks for solving most differentiation problems.
- 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
This section extends differentiation to higher-order and multivariable cases, helping you analyze more complex functions and systems.
- Higher Order Derivatives
- Partial Derivatives
- Total Derivative
- Application of Partial Derivatives
Learn how derivatives are applied to study change, optimize values, and analyze the behavior of functions in mathematics and real life.
- Application of Derivatives
- Rate of Change of Quantities
- Increasing Function
- Decreasing Function
- Critical Points
- Maxima and Minima
- Tangent and Normal
- Approximation
- Concavity and Points of Inflection
- Curve Sketching
- Mean Value Theorem
- Real-Life Application of 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
- Mean Value Theorem Practice Problems
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