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Basic Mathematics – I Richa Nandra, Lovely Professional University

Notes Unit 12: Successive Differentiation

CONTENTS
Objectives
Introduction

12.1 Successive Differentiation
12.2 Definition of Successive Differentiation
12.3 Summary

12.4 Keyword
12.5 Self Assessment
12.6 Review Questions
12.7 Further Readings

Objectives

After studying this unit, you will be able to:

Discuss successive differentiation
Differentiate problem related to successive differentiation

Introduction

Differentiation in math terms is the mathematical procedure of taking the derivative of a function.
A derivative of a function is a function that gives the slopes of the tangent lines to each point of
the curve representative of the function on a graph. We have seen that the derivative of a
function of x is in general also a function of x. This new function may also be differentiable, in
which case the derivative of the first derivative is called the second derivative of the original
function. Similarly, the derivative of the second derivative is called the third derivative; and so
th
on to the n derivative. Thus, if
2
d dy d y
=
dx dx dx 2
2
3
d d dy d d y d y
=
dx dx dx dx dx 2 dx 3
n
d d n 1 y d y
=
dx dx n 1 dx n
12.1 Successive Differentiation

If y = f(x) is a differentiable function then by differentiating it w.r.t. x, we get

dy
f x ...(i)
dx

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