Calculus I
Derivitives

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Lessons
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Part 1: Review

1-1 Functions

1-2 Inverse Functions

1-3 Trig Functions

1-4 Solving Trig Equations

1-5 Exponential Functions

1-6 Logarithm Functions

1-7 Exponential and Logarithm Equations

1-8 Common Graphs

Part 2: Limits

2-1 Tangent Lines and Rates of Change

2-2 The Limit

2-3 One-Sided Limits

2-4 Limit Properties

2-5 Computing Limits

2-6 Limits Involving Infinity

2-7 Continuity

2-8 The Definition of the Limit

Part 3: Derivatives

3-1 The Definition of the Derivative

3-2 Interpretation of the Derivative

3-3 Differentiation Formulas

3-4 Product and Quotient Rule

3-5 Derivatives of Trig Functions

3-6 Derivatives of Exponential and Logarithm Functions

3-7 Derivatives of Inverse Trig Functions

3-8 Derivatives of Hyperbolic Trig Functions

3-9 Chain Rule

3-10 Implicit Differentiation

3-11 Related Rates

3-12 Higher Order Derivatives

3-13 Logarithmic Differentiation

Part 4: Applications of Derivatives

Critical Points

Minimum and Maximum Values

Finding Absolute Extrema

The Shape of a Graph, Part I

The Shape of a Graph, Part II

The Mean Value Theorem

Optimization

L`Hospital`s Rule and Indeterminate Forms

Linear Approximations

Differentials

Newton`s Method

Part 5: Integrals

Indefinite Integrals

Computing Indefinite Integrals

Substitution Rule for Indefinite Integrals

More Substitution Rule

Area Problem

Definition of the Definite Integral

Computing Definite Integrals

Substitution Rule for Definite Integrals

Part 6: Applications of Integrals

Average Function Value

Area Between Curves

Volumes of Solids of Revolution / Method of Rings

Volumes of Solids of Revolution/Method of Cylinder

Work

Part 6:  Extras

Proof of the Product Rule

Proof of Quotient Rule

Types of Infinity

Summation Notation

Constant of Integration

Area and Volume Formulas

About These Lessons

The primary content for these lessons is provided courtesy of Paul's Online Math Notes and Lamar University.