VIII. Differential Calculus

Unit 6: Limits

6.1

Limits

6.2

[HL] The Existence of Limits

6.3

[HL] Limits at Infinity

6.4

[HL] Trigonometric Limits

6.5

[HL] Continuity

Unit 7: Differential Calculus

7.1

The Derivative Function

7.2

[HL] Differentiability & Continuity

Unit 8: Rules of Differentiation

8.1

Simple Rules for Differentiation

8.2

Chain Rule

8.3

Product Rule and Quotient Rule

8.4

Derivatives of Exponential Functions

8.5

Derivatives of Logarithmic Functions

8.6

Derivatives of Trigonometric Functions

8.7

[HL] Derivatives of Reciprocal Trig Functions

8.8

[HL] Derivatives of Inverse Trigonometric Functions

8.9

Second & Higher Derivatives

8.10

[HL] Implicit Differentiation

Unit 9: Properties of Curves

9.1

Tangents and Normals

9.2

Increasing & Decreasing Functions

9.3

Stationary Points

9.4

Shape and Inflection Points

9.5

[HL] L'Hôpital's Rule

Unit 10: Applications of Derivatives

10.1

Rates of Change

10.2

Optimization

10.3

[HL] Related Rates