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Title Transcription
ビブンホウ ノ 1 キホン コウシキ ノ ショウメイ ノ キョウジュホウ ニツイテ
Title Alternative (English)
On the Method of Teaching How to Prove a Fundamental Formula of Differentiation
File
language
jpn
Author
Singu, Tadao
Description
Almost every book of differential calculus treats the proof of the fundamental formula
(d/(dx))(x^n) = nx^<n-1>
as follows :
(1) Using the formula
x^n_2 - x^n_1 = (x_2-x_1)(x^<n-1>_2+x^<n-2>_2x_1+・・・+x^<n-1>_1)
(without any proof of this formula), or
(2)Using the binomial formula.
The former method has a defeat, that is, the used formula has no proof in the book, generally.
The latter method is quite complete but it needs the binomial formula to be proved. For this purpose we have to teach 'permutation and combination' throughly, although it takes much time and it decreases ordiuary students' interest in mathematics and let them feel weary. To avoid these I advise to use the following metbod :
First derive the formulae of differentiation of the sum, the product, and the quotient of two functions and of the composite function.※ Then with the mathematical induction and these formulae the derivative of x^n would be obtained easily without the use of the binomial theorem.
※ If n is limited to be an integer, this is not necessary.
Journal Title
島根農科大学研究報告
Volume
3
Start Page
125
End Page
126
ISSN
05598311
Published Date
1955-05-30
NCID
AN00108241
Publisher
島根農科大学
Publisher Aalternative
The Shimane Agricultural College
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Life and Environmental Science
Remark
A,Bを含む
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