5.1 Limits

1. Definition & Notation 🔧

2. Continuity

3. Arithmetic Properties

4. Limits of Lines & Asymptotes

5. Squeeze Theorem

6. Limits of Trig Functions 🔧

7. Limits Related to Zero & Infinity

5.2 Mathematical Constants

1. Proof of $\pi$ 🔧

2. The Natural Number $e$ 🔧

3. The Golden Ratio $\phi$ 🔧

4. The Plastic Ratio 🔧

5.3 Differentiation

• Derivative Definition & Function
• Notation
• Tangent Line
• Differentiability
• First Derivative Use
• Second Derivative Use

5.4 Derivatives Common Rules

• Arithmetic Properties
• Product Rule
• Quotient Rule
• Power Rule
• Mean Value Theorem for Derivatives
• Implicit Differentiation (Chain Rule)
• Derivative of an Invserse Function
• L'Hôpital's Rule
• Derivative of $e$ Exponents
• Derivative of Logarithmic Functions
• Derivative of Exponential Functions
• Derivative of a Variable Raised to Itself

5.5 Trigonometric Derivatives

• $d/dx \sin(x)$
• $d/dx \cos(x)$
• $d/dx \tan(x)$
• $d/dx \cot(x)$
• $d/dx \sec(x)$
• $d/dx \csc(x)$
• $d/dx \sin^{-1}(x)$
• $d/dx \cos^{-1}(x)$
• $d/dx \tan^{-1}(x)$
• $d/dx \cot^{-1}(x)$
• $d/dx \sec^{-1}(x)$
• $d/dx \csc^{-1}(x)$

5.6 Complex Analysis & Trigonometry

• Complex Number System
• Analytic Trig Functions
• Analytic Trig Inverses

5.7 Hyperbolic Trigonometry

• Unit Hyperbola Definitions
• Hyperbolic Common Identities
• Limits of Hyperbolic Functions
• Derivatives of Hyperbolic Functions
• Real Version of Euler's Formula
• Analytic Hyperbolic Functions
• Analytic Hyperbolic Inverses

5.8 Parametric & Polar Differentiation