nd and simplify 2² x² (f(x) g(x)). O d² O −(ƒ (x) g(x)) = ƒ” (x) g(x)+ f (x) g″ (x) Hint 2² -(f(x) g(x)) = : ƒ'' (x) g(x)+2ƒ′ (x) g′ (x)+ ƒ (x) g″ (x) az −(ƒ (x) g(x)) = ƒ'' (x) g′ (x)+2ƒ' (x) g′ (x) + ƒ' (x) g″ (x) d² −(ƒ (x) g(x)) = ƒ” (x) g′ (x)+ ƒ' (x) g″ (x) dx² 5(ƒ (x) g(x)) = ƒ' (x) g(x)+ ƒ” (x) g′ (x)+ƒ' (x) g″ (x)+ ƒ (x) g″ (x) eTextbook and Media

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Find and simplify
5(ƒ (x) g(x)).
dx²
dx²
Hint
(ƒ (x) g(x))
=
ƒ'' (x) g(x)+ ƒ (x) g″ (x)
d²
−(ƒ (x) g(x)) = ƒ” (x)g (x)+2ƒ' (x) g′ (x)+ ƒ (x) g″ (x)
dx²
-(f(x) g(x)) = ƒ” (x) g′ (x)+2ƒ' (x) g'(x) + f'(x) g" (x)
eTextbook and Media
(f(x) g(x)) = f'(x) g' (x)+ f' (x) g" (x)
dx²
d²
Ƒ(ƒ (x) g(x)) = ƒ' (x) g(x)+ ƒ'' (x) g′ (x)+ ƒ' (x) g″ (x)+ ƒ (x) g″ (x)
dx²
Transcribed Image Text:Find and simplify 5(ƒ (x) g(x)). dx² dx² Hint (ƒ (x) g(x)) = ƒ'' (x) g(x)+ ƒ (x) g″ (x) d² −(ƒ (x) g(x)) = ƒ” (x)g (x)+2ƒ' (x) g′ (x)+ ƒ (x) g″ (x) dx² -(f(x) g(x)) = ƒ” (x) g′ (x)+2ƒ' (x) g'(x) + f'(x) g" (x) eTextbook and Media (f(x) g(x)) = f'(x) g' (x)+ f' (x) g" (x) dx² d² Ƒ(ƒ (x) g(x)) = ƒ' (x) g(x)+ ƒ'' (x) g′ (x)+ ƒ' (x) g″ (x)+ ƒ (x) g″ (x) dx²
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