5.1 Differentiation 1
Lecture Outline
Reference
Introduction
Tangent lines
Tangent lines
Tangent lines
Tangent lines
Tangent lines
Rates of change
Rates of change
Rates of change
Rates of change
Rates of change
Rates of change
Derivative function
Derivative function
Derivative function
Derivative function
Derivative function
Derivative function
Derivative function
Differentiability
Differentiability
Differentiability
Differentiability
Differentiability
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Differentiation rules
Learning outcomes
Formulae
Preview activity: Differentiation 2
2.40M
Category: mathematicsmathematics

Differentiation. A “derivative”,

1. 5.1 Differentiation 1

Foundation Year Program
NUFYP Mathematics
5.1 Differentiation 1
Viktor Ten
2019-2020

2. Lecture Outline

Foundation Year Program
Lecture Outline
Rates of
change
Defining
derivatives
using limits
Tangent lines
and slopes
Definition of a
derivative of a
function
Average rate
of changes
Instantaneous
rate of
changes
Differentiation
using limits
Differentiability
Differentiation
rules
Constant
Power function
Constant-times
function
Sum & difference
Product
Quotient
2019-2020

3. Reference

Foundation Year Program
Reference
Anton, H., Bivens I., Davis, S.
Calculus Early Transcendentals, 10th edition
https://library.nu.edu.kz/.RMSearch/URL?type=search&book=10945
2019-2020

4. Introduction

Foundation Year Program
Introduction
Many real-world phenomena involve changing quantities:
• the speed of a rocket,
• the inflation of currency,
• the number of bacteria in a culture,
• the shock intensity of an earthquake,
• the voltage of an electrical signal, and so forth.
In this lecture we will develop the concept of a “derivative”,
which is the mathematical tool for studying the rate at
which one quantity changes relative to another.
2019-2020

5. Tangent lines

Foundation Year Program
Tangent lines
Consider a point
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