W-2. (f g)'(x) = f'(x) · g(x) + g'(x)f(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PROVE number 2 please ?
![Ho W-2. (f g)'(x) = f'(x) · g(x) + g'(x)f(x)
3. (2) (x) = 9(x)f'(x)-f(x)g'(x)
(ø(x))*
g(x) # 0
Proof :
(S + g)(x + h) – ( +g)(x)
1. (f + g)'(x) = ļim
h-0
h
f(x + h) + g(x + h) – f(x) - g(x)
= lim
h-0
%3D
h
f(x + h) – f(x)+ g(x + h) – g(x)
= lim
h-0
h
f(x + h) - f(x)
= lim
h-0
g(x + h) – g(x)
+ ļim
h-0
h
h
= f(x) + ý (x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e35a088-ac88-4bc6-8102-24be224e730b%2F3b3ae881-7b99-4529-abeb-539d5739da33%2Fjhhqz0m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ho W-2. (f g)'(x) = f'(x) · g(x) + g'(x)f(x)
3. (2) (x) = 9(x)f'(x)-f(x)g'(x)
(ø(x))*
g(x) # 0
Proof :
(S + g)(x + h) – ( +g)(x)
1. (f + g)'(x) = ļim
h-0
h
f(x + h) + g(x + h) – f(x) - g(x)
= lim
h-0
%3D
h
f(x + h) – f(x)+ g(x + h) – g(x)
= lim
h-0
h
f(x + h) - f(x)
= lim
h-0
g(x + h) – g(x)
+ ļim
h-0
h
h
= f(x) + ý (x)
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