Chapter 16: Differentiation

16.1: 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

16.2: 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

16.3: 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

16.4: 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

16.5: Derivative of Inverse Functions

1. Derivative of Inverse Functions

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

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

16.7: Differentiation of Implicit Relations

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

16.8: 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

16.9: 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

16.10: Derivative of Exponential Functions

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

16.11: Derivative of Logarithmic Functions

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

16.12: Logarithmic Differentiation

1. Problem Solving-Logarithmic Functions

16.13: Derivative of Hyperbolic Functions

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

16.14: 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

16.15: 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

16.16: 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

16.17: 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

16.18: Geometrical Interpretation of a Derivative

1. Geometrical Interpretation of a Derivative

16.19: Increasing and Decreasing Functions

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

16.20: Relative Extrema

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

16.21: 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