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Let f and g be the functions in the table below. g(x) 2 3 X 1 2 3 f(x) 3 1 2 1 (a) If F(x) = f(f(x)), find F '(3). F'(3) = X f'(x) 4 5 7 g'(x) 6 7 9

Let f and g be the functions in the table below. g(x) 2 3 X 1 2 3 f(x) 3 1 2 1 (a) If F(x) = f(f(x)), find F '(3). F'(3) = X f'(x) 4 5 7 g'(x) 6 7 9

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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Let f and g be the functions in the table below. f(x) g(x) 3 2 1 3 2 1 (a) If F(x) = f(f(x)), find F '(3). F'(3) X = x 1 2 3 (b) If G(x) = g(g(x)), find G'(1). G'(1) = f'(x) 4 5 7 g'(x) 6 7 9
Transcribed Image Text:Let f and g be the functions in the table below. f(x) g(x) 3 2 1 3 2 1 (a) If F(x) = f(f(x)), find F '(3). F'(3) X = x 1 2 3 (b) If G(x) = g(g(x)), find G'(1). G'(1) = f'(x) 4 5 7 g'(x) 6 7 9
Expert Solution
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the first function is 

F\left(x\right)=f\left(f\left(x\right)\right)

take derivative

F'\left(x\right)=\frac{d}{dx}\left[f\left(f\left(x\right)\right)\right]

F'\left(x\right)=f'\left(f\left(x\right)\right)\frac{d}{dx}\left[f\left(x\right)\right]

F'\left(x\right)=f'\left(f\left(x\right)\right)\cdot f'\left(x\right)

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