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Pavitar Parkash Singh, Lovely Professional University Unit 6: Differentiation: Partial

Unit 6: Differentiation : Partial Note

CONTENTS

Objectives
Introduction
6.1 Differentiation of a Function in Respect to Other Function
6.2 Summary
6.3 Keywords
6.4 Review Questions
6.5 Further Readings

Objectives

After reading this unit students will be able to:
z Understand the Method of Differentiation of a Function in Respect to other Function.

Introduction

Differential coefficient of the first function relative to some other function is the ratio of the differential
coefficient of the first function with respect to x to the differential coefficient of the second function
with respect to x.

6.1 Differentiation of a Function in Respect to Other Function

x
Suppose y 1 f 1 () and y 2 f 2 ()
x
That is y and y are the functions of x, on differentiating both with respect to x
1 2
dy 1 f c()x and dy 2 f c()x
dx 1 dx 1
dy
Now the differential coffiecient of y with respect to y is 1
1 2 dy 2

dy 1
dy 1 dx f 1 c()x
Notes dy 2 dy 2 f 2 c() x
dx

dy 1 Differential coefficient of y 1 with respect to
x
Therefore dy 2 Differential coefficient of y 2 with respect to x

Did u know? Differential coefficient of the first function relative to some other function is
the ratio of the Differential coefficient of the first function with respect to x to
the Differential coefficient of the second function with respect to x.

LOVELY PROFESSIONAL UNIVERSITY 97