QI: In Leibnitz theorem, If f and g are functions of a variable x, then nth derivative of (f.g) can be defined as: (f. g)(n) = f (n) g + "cf(n-1)(g)(1) + Where (f.g)(n) = D"(f.g), D" - "c2f (n-2)(g)(2) +.+ "c,f(1)(g)(n-1) + f. g(n) and "c, d" n! %3D %3D dx" (n-r)! r! Prove that p(n) is true for all positive integral value of n.
QI: In Leibnitz theorem, If f and g are functions of a variable x, then nth derivative of (f.g) can be defined as: (f. g)(n) = f (n) g + "cf(n-1)(g)(1) + Where (f.g)(n) = D"(f.g), D" - "c2f (n-2)(g)(2) +.+ "c,f(1)(g)(n-1) + f. g(n) and "c, d" n! %3D %3D dx" (n-r)! r! Prove that p(n) is true for all positive integral value of n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:QI: In Leibnitz theorem, If f and g are functions of a variable x, then nth
derivative of (f.g) can be defined as:
(f. g)(n) = f(n)g + "c,f (n-1)(g)(1) + "c,f (n-2)(
Where (f.g)(n) = D"(f.g), D" -
g)(2) + ... + "cif(1)(g)(n-1) + f. g(m)
d"
and "c,
n!
%3D
%3D
(n-r)! r!
Prove that p(n) is true for all positive integral value of n.
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