Page 249 - DMTH201_Basic Mathematics-1

Basic Mathematics – I Varun Kumar, Lovely Professional University

Notes Unit 9: Differential Calculus

CONTENTS

Objectives
Introduction

9.1 Differentiation
9.1.1 Derivative of a Function - Method of First Principles

9.2 General Theorems on Derivatives: (Without Proof)
9.3 Derivatives of Standard Functions

9.4 Function of a Function (or Composite Function)
9.5 Implicit Functions

9.6 Summary
9.7 Keywords

9.8 Self Assessment
9.9 Review Questions

9.10 Further Readings

Objectives

After studying this unit, you will be able to:

Discuss the derivative of a function
Explain the certain basic rules that can be used to find the derivatives of various types of
composite functions

Introduction

Given a function, we are often interested to know how the change in one variable corresponds
to changes in the other. The questions relating to rates of changes require the introduction to the
concept of derivatives. The maxima and minima of functions, an important application of
derivatives, will also be discussed in this unit.
In this unit, we study various methods of differentiation and its application. It deals with the
study of change.

9.1 Differentiation

x
f ( ) f ( )
a
A function f(x) is said to be differentiable at x = a if lim exists. This limit is denoted by
x a x a
f (a) and

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