Page 273 - DMTH201_Basic Mathematics-1

Basic Mathematics – I Richa Nandra, Lovely Professional University

Notes Unit 10: Logarithmic Differentiation

CONTENTS
Objectives
Introduction

10.1 Logarithmic Differentiation
10.2 Logarithmic Differentiation Problems
10.2.1 Properties of the Natural Logarithm

10.2.2 Avoid the Following List of Common Mistakes
10.3 Summary
10.4 Keyword
10.5 Self Assessment
10.6 Review Questions

10.7 Further Readings

Objectives

After studying this unit, you will be able to:
Discuss lop logarithmic differentiation

Explain problem retated to logarithmic differentiation
Introduction

A function which is the product or quotient of a number of functions. A function of the form the
[ f ( x ) ]g ( x ) where f ( x ) and g ( x ) are both derivable, it is usually advisable to take logarithm
of the function first and then differentiate. The process is known as the logarithmic differentiation.

10.1 Logarithmic Differentiation

g x
To differentiate a function of the form f x or a f x , we use a method called Logarithmic
differentiation.
g x
To find the derivative of the functions f x and a f x .

g x
(i) Let y f x
Taking logarithms, we get
logy g ( )log f x
x
Differentiate w.r.t. x
1 dy 1
g x f x log f x .g x
y dx f x

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