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If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does no exist, explain why. (If an answer does not exist, enter DNE.) -2 (a) u (1) = (b) v'(1) = y 10 8 O It does exist. (c) w'(1) - 2 X O It does exist. O u(1) does not exist because f'(5) does not exist. O u'(1) does not exist because g'(1) does not exist. O u'(1) does not exist because f'(6) does not exist. O u'(1) does not exist because g'(5) does not exist. 4 6 8 10 O v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. O v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. O It does exist. O w'(1) does not exist because f'(1) does not exist. Ow'(1) does not exist because g'(1) does not exist. O w'(1) does not exist because f'(5) does not exist. Ow'(1) does not exist because g'(5) does not exist. X ( t

If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does no exist, explain why. (If an answer does not exist, enter DNE.) -2 (a) u (1) = (b) v'(1) = y 10 8 O It does exist. (c) w'(1) - 2 X O It does exist. O u(1) does not exist because f'(5) does not exist. O u'(1) does not exist because g'(1) does not exist. O u'(1) does not exist because f'(6) does not exist. O u'(1) does not exist because g'(5) does not exist. 4 6 8 10 O v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. O v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. O It does exist. O w'(1) does not exist because f'(1) does not exist. Ow'(1) does not exist because g'(1) does not exist. O w'(1) does not exist because f'(5) does not exist. Ow'(1) does not exist because g'(5) does not exist. X ( t

Calculus: Early Transcendentals
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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If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does not exist, explain why. (If an answer does not exist, enter DNE.) -2 (a) u (1) = (b) v'(1) = y 10 8 O It does exist. (c) w'(1) - 2 x O It does exist. Ou(1) does not exist because f'(5) does not exist. O u'(1) does not exist because g'(1) does not exist. O u'(1) does not exist because f'(6) does not exist. O u'(1) does not exist because g'(5) does not exist. 4 6 8 O v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. O v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. O It does exist. O w'(1) does not exist because f'(1) does not exist. Ow'(1) does not exist because g'(1) does not exist. O w'(1) does not exist because f'(5) does not exist. Ow(1) does not exist because g'(5) does not exist. 10 X ↑ W
Transcribed Image Text:If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does not exist, explain why. (If an answer does not exist, enter DNE.) -2 (a) u (1) = (b) v'(1) = y 10 8 O It does exist. (c) w'(1) - 2 x O It does exist. Ou(1) does not exist because f'(5) does not exist. O u'(1) does not exist because g'(1) does not exist. O u'(1) does not exist because f'(6) does not exist. O u'(1) does not exist because g'(5) does not exist. 4 6 8 O v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. O v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. O It does exist. O w'(1) does not exist because f'(1) does not exist. Ow'(1) does not exist because g'(1) does not exist. O w'(1) does not exist because f'(5) does not exist. Ow(1) does not exist because g'(5) does not exist. 10 X ↑ W
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