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Theorem: Product Rule If f(x) = F(x)S(x) is the product of differentiable functions, then f'(x) = S(x)F'(x) F(x)S' (x) [S(x)]² O f'(x) = F(x)S' (x) + S(x)F' (x) O f'(x) = F'(x)S' (x) + S(x)F(x) O f'(x) = F(x)S' (x) – S(x)F" (x) O f'(x) = F'[S(x)]S'(x) O f'(x) = F'(x)S" (x)

Theorem: Product Rule If f(x) = F(x)S(x) is the product of differentiable functions, then f'(x) = S(x)F'(x) F(x)S' (x) [S(x)]² O f'(x) = F(x)S' (x) + S(x)F' (x) O f'(x) = F'(x)S' (x) + S(x)F(x) O f'(x) = F(x)S' (x) – S(x)F" (x) O f'(x) = F'[S(x)]S'(x) O f'(x) = F'(x)S" (x)

Advanced Engineering Mathematics
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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Theorem: Product Rule If f(x) = F(x)S(x) is the product of differentiable functions, then f'(x) = S(x)F'(x) F(x)S' (x) [S(x)]² O f'(x) = F(x)S' (x) + S(x)F' (x) O f'(x) = F'(x)S' (x) + S(x)F(x) ○ f'(x) = F(x)S" (x) – S(x)F' (x) - ○ f'(x) = F'[S(x)]S′(x) O f'(x) = F'(x)S" (x)
Transcribed Image Text:Theorem: Product Rule If f(x) = F(x)S(x) is the product of differentiable functions, then f'(x) = S(x)F'(x) F(x)S' (x) [S(x)]² O f'(x) = F(x)S' (x) + S(x)F' (x) O f'(x) = F'(x)S' (x) + S(x)F(x) ○ f'(x) = F(x)S" (x) – S(x)F' (x) - ○ f'(x) = F'[S(x)]S′(x) O f'(x) = F'(x)S" (x)
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