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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