Chapter 2: Differentiation

2.1: Introduction

1. Introducing Dependent and Independent Variables
2. Average Rate of Change
3. Derivative of a Function
4. More on Derivative of a Function
5. Notation for Derivative
6. Geometrical Interpretation of a Derivative
7. More on Geometrical Interpretation of Derivative

2.2: Finding f'(x) from Definition of Derivative

1. Derivative by First Principle
2. More on Derivative by First Principle
3. Problem1-Derivative by First Principle
4. Problem2-Derivative by First Principle

2.3: Theorems on Definition

1. Derivative of a Constant Function
2. Power Rule for Differentiation
3. More on Power Rule for Differentiation
4. Problem-Power Rule for Differentiation
5. Problem1-Power Rule for Differentiation
6. Derivative of a sum or Difference of Functions
7. Problem1-Derivative of a sum or Difference of Functions
8. Derivative of Product
9. Problem1-Derivative of Product
10. Derivative of a Quotient
11. More on Derivative of a Quotient
12. Problem1a-Derivative of Quotient

2.4: The Chain Rule

1. Differentiation by Chain Rule
2. More on Differentiation by Chain Rule
3. Problem1-Differentiation by Chain Rule
4. Problem2-Differentiation by Chain Rule

2.5: Derivative of Inverse Functions

1. Derivative of Inverse Functions

2.6: Derivative of Functions Given in the Form of Parametric Equations

1. Derivative of Parametric Equations
2. Problem1-Derivative of Parametric Equations

2.7: Differentiation of Implicit Relations

1. Implicit Differentiations
2. Problem-Implicit Differentiations
3. Problem-Implicit Differentiations

2.8: Derivatives of Trigonometric Functions

1. Derivative of Trigonometric Functions
2. More on Derivative of Trigonometric Functions
3. More Stuff on Derivative of Trigonometric Functions
4. Problem1-Derivative of Trigonometric Functions
5. Problem2-Derivative of Trigonometric Functions
6. Problem3-Derivative of Trigonometric Functions

2.9: Derivatives of Inverse Trigonometric Functions

1. Derivative of Inverse Trigonometric Functions
2. More on Derivative of Inverse Trigonometric Functions
3. Problem1-Derivative of Inverse Trigonometric Functions
4. Problem2-Derivative of Inverse Trigonometric Functions
5. Problem3-Derivative of Inverse Trigonometric Functions

2.10: Derivative of Exponential Functions

1. Derivative of Exponential Functions
2. Problem1-Derivative of Exponential Functions

2.11: Derivative of Logarithmic Functions

1. Derivative of Logarithmic Functions
2. Problem1-Derivative of Logarithmic Functions

2.12: Logarithmic Differentiation

1. Problem Solving-Logarithmic Functions

2.13: Derivative of Hyperbolic Functions

1. Derivative of Hyperbolic Functions
2. More on Derivative of Hyperbolic Functions
3. Problem1-Derivative of Hyperbolic Functions

2.14: Derivatives of the Inverse Hyperbolic Functions

1. Derivatives of the Inverse Hyperbolic Functions
2. More on Derivatives of the Inverse Hyperbolic Functions
3. Problem1-Derivatives of the Inverse Hyperbolic Functions

2.15: Successive Differentiation Or Higher Derivatives

1. Introducing Higher Order Differentiation
2. Problem1-Introducing Higher Order Differentiation
3. Problem2-Introducing Higher Order Differentiation
4. Problem3-Introducing Higher Order Differentiation
5. Problem4-Introducing Higher Order Differentiation

2.16: Series Expansion of Functions

1. Introducing Maclaurin's Theorem
2. More on Maclaurin's Theorem
3. Problem1-Introducing Maclaurin's Theorem
4. Problem2-Introducing Maclaurin's Theorem

2.17: Tailor Series Expansion of Functions

1. Tailor's Theorem
2. More on Tailor's Theorem
3. Problem1a-Tailor's Theorem
4. Problem2-Tailor's Theorem

2.18: Geometrical Interpretation of a Derivative

1. Geometrical Interpretation of a Derivative

2.19: Increasing and Decreasing Functions

1. Increasing and Decreasing Functions
2. More on Increasing and Decreasing Functions
3. Problem1-Increasing and Decreasing Functions

2.20: Relative Extrema

1. Introducing Relative Extrema
2. Problem1-Introducing Relative Extrema

2.21: Critical Values of Critical Points

1. Relative Maxima and Minima
2. Problem2-Relative Maxima and Minima
3. Critical Values and Critical Points
4. Point of Inflexion
5. Second Derivative Test and Concavity
6. More on Second Derivative Test and Concavity
7. Problem Solving-Second Derivative Test and Concavity
8. Differential-Maxima and Minima Problems
9. Problem1a-Second Derivative and Its Applications
10. Problem2a-Second Derivative and Its Applications
11. Problem3a-Second Derivative and Its Applications