Affiliation:
1. The University of Western Ontario, London, Ontario, Canada
Abstract
The following problem is one that many first year calculus students find quite difficult:Given a formula for a function
f
in a variable
x,
find a formula for its
n
th derivative.
Example 1.1:
[1, p. 229] If
f
(
x
) =
x
m
,
(1)then its
n
th derivative is
f
(
n
)
(
x
) =
m-
n
x
m-n
,
(2)where
m-
n
= m
(
m
- 1) (
m
- 2) ⋅⋅⋅ (
m - n
+ 1).The difficulties for students include, first, the discovery of a formula valid for all integers
n
and, second, the proof (for example, by induction) that the formula is correct. Can computer algebra systems do better?It is certain that Macsyma could (we remember commands for infinite Taylor series expansion of elementary functions, and that necessarily involves discovering a correct formula for the
n
th derivative of the input). Currently, Maple cannot---at least, not without help, just with one command, now that the Formal Power Series package in the share library is no longer supported.
Publisher
Association for Computing Machinery (ACM)
Reference2 articles.
1. G. H. HARDY A Course of Pure Mathematics Cambridge University Press 10th ed. 1952. G. H. HARDY A Course of Pure Mathematics Cambridge University Press 10th ed. 1952.
2. W. RUDIN Real And Complex Analysis McGraw-Hill Book Company 1987. W. RUDIN Real And Complex Analysis McGraw-Hill Book Company 1987.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Blends in Maple;Communications in Computer and Information Science;2021
2. Revisiting Gilbert Strang's "a chaotic search for
i
";ACM Communications in Computer Algebra;2019-09-18