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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 doe not exist, enter DNE.) 8 4 2 x -2 2 4 6 8 10 (a) u'(1) It does exist. ○ u'(1) does not exist because f'(6) does not exist. u'(1) does not exist because g'(1) does not exist. Ou'(1) does not exist because f'(7) does not exist. Ou'(1) does not exist because g'(6) does not exist. (b) v'(1) It does exist. v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. (c) w'(1) = It does exist. Ow'(1) does not exist because f'(1) does not exist. w'(1) does not exist because g'(1) does not exist. w'(1) does not exist because f'(6) does not exist. w'(1) does not exist because g'(6) does not exist.

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 doe not exist, enter DNE.) 8 4 2 x -2 2 4 6 8 10 (a) u'(1) It does exist. ○ u'(1) does not exist because f'(6) does not exist. u'(1) does not exist because g'(1) does not exist. Ou'(1) does not exist because f'(7) does not exist. Ou'(1) does not exist because g'(6) does not exist. (b) v'(1) It does exist. v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. (c) w'(1) = It does exist. Ow'(1) does not exist because f'(1) does not exist. w'(1) does not exist because g'(1) does not exist. w'(1) does not exist because f'(6) does not exist. w'(1) does not exist because g'(6) does not exist.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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 doe not exist, enter DNE.) 8 4 2 x -2 2 4 6 8 10 (a) u'(1) It does exist. ○ u'(1) does not exist because f'(6) does not exist. u'(1) does not exist because g'(1) does not exist. Ou'(1) does not exist because f'(7) does not exist. Ou'(1) does not exist because g'(6) does not exist. (b) v'(1) It does exist. v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. (c) w'(1) = It does exist. Ow'(1) does not exist because f'(1) does not exist. w'(1) does not exist because g'(1) does not exist. w'(1) does not exist because f'(6) does not exist. w'(1) does not exist because g'(6) does not exist.
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 doe not exist, enter DNE.) 8 4 2 x -2 2 4 6 8 10 (a) u'(1) It does exist. ○ u'(1) does not exist because f'(6) does not exist. u'(1) does not exist because g'(1) does not exist. Ou'(1) does not exist because f'(7) does not exist. Ou'(1) does not exist because g'(6) does not exist. (b) v'(1) It does exist. v'(1) does not exist because f'(1) does not exist. O v'(1) does not exist because g'(1) does not exist. v'(1) does not exist because f'(2) does not exist. O v'(1) does not exist because g'(2) does not exist. (c) w'(1) = It does exist. Ow'(1) does not exist because f'(1) does not exist. w'(1) does not exist because g'(1) does not exist. w'(1) does not exist because f'(6) does not exist. w'(1) does not exist because g'(6) does not exist.
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