G12 Calculus And Vectors (Mcv4U)

Chapter 2 - Derivatives

What you'll learn

Understand and determine derivatives of polynomial and simple rational functions from first principles

Identify examples of functions that are not differentiable

Justify and use the rules for determining derivatives

Identify composition as two functions applied in succession

Determine the composition of two functions expressed in notation, and decompose a given composite function into its parts

Use the derivative to solve problems involving instantaneous rates of change

Requirements

G11 Functions (MCR3U), G12 Advanced Functions (MHF4U)

Description

Imagine a driver speeding down a highway, at 140 km/h. He hears a police siren and is quickly pulled over. The police officer tells him that he was speeding, but the driver argues that because he has travelled 200 km from home in two hours, hisaverage speed is within the 100 km/h limit. The driver’s argument fails because police officers charge speeders based on their instantaneous speed, not their average speed.There are many other situations in which the instantaneous rate of change is more important than the average rate of change. In calculus, the derivative is a tool for finding instantaneous rates of change. This chapter shows how the derivative can be determined and applied in a great variety of situations.In this chapter, you will learn and understand below content• understand and determine derivatives of polynomial and simple rational functions from first principles• identify examples of functions that are not differentiable• justify and use the rules for determining derivatives (Product Rule, Quotient Rule, Chain Rule, etc.)• identify composition as two functions applied in succession• determine the composition of two functions expressed in notation, and decompose a given composite function into its parts• use the derivative to solve problems involving instantaneous rates of change

Overview

Section 1: Derivatives

Lecture 1 The Derivative Function

Lecture 2 The Derivatives of Polynomial Functions

Lecture 3 The Product Rule

Lecture 4 The Quotient Rule

Lecture 5 The Derivatives of Composite Functions

G11 and G12 students who have chosen Calculus and Vectors (MCV4U)