Differentiation And Its Application

This research is mainly on one aspect of calculus called differentiation and its application. The study is organized into five chapters, covering the introduction, fundamentals of calculus, detailed analysis of differentiation and its applications, summary and conclusion. It investigates into historical contributions to calculus, highlighting the work of pioneers such as Newton and Leibniz, who developed differentiation and integration into a structured mathematical discipline. The study emphasizes the practical relevance of differentiation in modern science, technology, and industries, where understanding the rate of change is essential for optimizing production and resource distribution. By reviewing its operational principles, this research underscores the importance of differentiation in addressing mathematical problems and real-world challenges.

Certification
Dedication
Acknowledgment
Table of content
Abstract

CHAPTER ONE
Introduction
Scope of the study and limitation
Purpose of the study
Significance of the study

CHAPTER TWO
Literature review
Fundamental of calculus
Functions of a single variable and their graphs
Graph of a function
The rate of change of a function
Limits and continuity
Theory on limits
Infinite limits and limits at infinity Continuity

CHAPTER THREE
Differentiation
Differentiation as a limit of rate of change of elementary function
Gradient (straight line and curve)
Differentiation as a limit of rate of change of a function
Rules for differentiation
Differentiation of trigonometric function
Differentiation of a function of a function
Differentiation of implicit function
Differentiation of logarithmic, exponential and parametric function

CHAPTER FOUR
Application of differentiation
The tangent and normal to a curve
Maxima and minima point
Cure sketching
Point of inflexion

CHAPTER FIVE
Summary and conclusion
References.

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