Basic Differentiation Rules and Applications in Engineering

• Mathematics
• Higher Education (non-degree)

Basic Differentiation Rules and Applications in Engineering

                                                                                    Tues 24th Sep

Dr. Afrouz Mehr

Learning Objectives

At the end of the lesson, you will be able to:

1- Apply the Constant Rule to differentiate constant functions

2-Apply the Polynomial Rule to differentiate polynomial functions. 

3-Understand the application of differentiation in engineering, specifically in calculating rates of change such as velocity and acceleration.

4-solve basic differentiation problems involving polynomial expressions.

What do you already know about differentiation rules in engineering?

Overview of Differentiation Rules

Introduction to the Constant Rule and Polynomial Rule in differentiation

Application of Constant Rule

Examples demonstrating the application of the Constant Rule

If f(x) =k, then f'(x) = 0.

Example: 

                                               Differentiate f(x) = 5.

                                                   Answer: f'(x) = 0.

Application of Polynomial Rule

Examples demonstrating the application of the Polynomial Rule

If f(x) = ax^n, then f'(x) = n * ax^(n-1).

Example: 

                                      Differentiate f(x) = 3x^2.

                                              Answer: f'(x) = 6x.

Importance in Engineering

The importance of differentiation in engineering to calculate rates of change

For example, it is used to calculate velocity (rate of change of position) and acceleration (rate of change of velocity).

Problem Solving

Step-by-step solutions to differentiation problems using the rules:

1. Differentiate f(x) = 4x^3 ?

2. Differentiate f(x) = 7x^2 + 3x + 2 ?

Definition List

Constant Rule: 

Polynomial Rule: 

Differentiation: 

Rate of Change: 

Definition List

Constant Rule: A differentiation rule stating that the derivative of a constant function is zero. 

Polynomial Rule: A differentiation rule that describes how to find the derivative of a polynomial function, which involves multiplying the exponent by the coefficient and reducing the exponent by one. 

Differentiation: A mathematical process that calculates the rate of change of a function. 

Rate of Change: A measure of how a quantity changes over time, commonly used in engineering to describe phenomena like velocity and acceleration.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.