## Grade 12 Calculus and Vectors

Chapter 2: Derivatives

Derivative is the instantaneous rate of change and sometimes referred to as the rate of change (i.e. how fast or quickly is something changing). This chapter will look at the concept of derivative, and the procedure for finding derivatives of functions. The process of finding derivative is called differentiation, and we will start by differentiating polynomials and rational functions using sum, difference, product, quotient, power and chain rules as well as, composite function differentiation rule. It is highly recommended that students take the time to master these techniques because this is the very foundation from which all Calculus topics will build upon.

HINT: It is evident from the chapter and overall course reviews that** slope = m = rise/run = ΔY / ΔX = rate of change = tangent = limits = gradient**. Now, to add a new word to the list: yes, you’ve guessed it- its** “DERIVATIVE!” **Derivative is similar to all of the previously mentioned terms, but it’s more synonymous to instantaneous rate of change.

**
2.1 Introduction to Derivatives (limit of f(x) as h—>0)
2.2 Derivatives: Power Rule
2.3 Derivatives: Sum and Difference Rules
2.4 Derivatives: Product Rule
2.5 Derivatives: Quotient Rule
2.6 Derivatives: Chain Rule [Composite functions]
2.7 Derivatives: Power Rule for Composite Functions
**

## Grade 12 Calculus and Vectors

Chapter 1: Introduction to* Calculus *and Vectors

Chapter 2: Derivatives

2.1 Introduction to Derivatives (limit of f(x) as h→0)

2.2 Derivatives: Power and Constant Multiple Rules

2.3 Derivatives: Sum and Difference Rules

2.4 Derivatives: Product Rule

2.5 Derivatives: Quotient Rule

2.6 Derivatives: Chain Rule [Composite functions]

2.7 Derivatives: Power Rule for Composite Functions

Chapter 3: Applications of Derivatives

Chapter 4: Curve Sketching

Chapter 5: Derivatives of Trigonometric Functions

Chapter 6: Derivatives of Exponential Functions

Chapter 7: Introduction to * Vectors *

Chapter 8: Vector Operations and Applications

Chapter 9: Equations of Lines

Chapter 10: Equations of Planes

Chapter 11: Points, Lines and Planes

Videos for each topic contain a playlist, allowing you to choose the instructor and learning style to your liking. You can choose different videos in a topic by placing the mouse over the video and selecting a different video from the playlist. Videos of solutions to multiple example problems are also available to illustrate to students how each tools and techniques should be used.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

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