A Treatise on the Differential Calculus

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Deightons, 1846 - Differential calculus - 263 pages
 

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Contents

Differentiation of a function of any number of functions of a single variable
15
General theory of the differentiation of implicit functions of a single variable
18
Total differentiation of a function of functions of independent variables
19
Article Page 25 Partial differentiation of an explicit function of three variables one of which is a function of the other two
21
Partial differentiation of an explicit function of n + r variables r independent and n dependent
22
Partial differentiation of an implicit function of two independent variables
23
Simple functions
25
Differential coefficient of loga x
26
Differential coefficient of ar
28
Differential coefficient of sin a
29
Differential coefficient of tan x
30
Differential coefficient of sec x
31
Differential coefficient of sinx
32
Differential coefficient of cosx
33
Differential coefficient of cotx
34
Differential coefficient of cosecx
35
45 Illustrative examples
37
CHAPTER III
44
Change of the independent variable
46
Order of partial differentiations indifferent
50
Successive differentiation of an explicit function of two func tions of a single variable
52
Successive differentiation of an implicit function of a single variable
55
Successive total differentials
57
Successive differentiation of an explicit function of three vari ables one of which is a function of the other two
58
Change of variables
60
Transformation of one system of independent variables into another
61
Article Page
67
CHAPTER V
84
Failure of the method of differentials for the evaluatiou of
92
CHAPTER VI
99
Abbreviation of operation
107
CHAPTER VII
128
Another demonstration of Taylors theorein
133

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