Type your question here 19. -0.45 points My Notes I SEssCalcET2 2.5.057 If f and

Question

Type your question here

19. -0.45 points My Notes I SEssCalcET2 2.5.057 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 (a) u'(1) It does exist O u'(x) does not exist because f '(1) does not exist. O u (x) does not exist because g'(1) does not exist. O u'(x) does not exist because f 3) does not exist. O u (x) does not exist because g'(2) does not exist. (b) v(1) It does exist O v'(x) does not exist because f '(1) does not exist. O v'(x) does not exist because g (1) does not exist. O v'(x) does not exist because f '(3) does not exist. O v'(x) does not exist because g'(2) does not exist. (c) (1) It does exist O w'(x) does not exist because f (1) does not exist. O x) does not exist because g'(1) does not exist. O x) does not exist because f '(3) does not exist. O x) does not exist because g (2) does not exist. Need Help? Read It Watch It Chat About It 20 -0.45 points My Notes I SEssCalcET2 2.5.058.

Explanation / Answer

a) u'(x) = f'(g(x))*g'(x), so u'(1) = f'(g(1))*g'(1) = f'(3)*g'(1). Both of these exist, so u'(1) exists. b) v'(x) = g'(f(x))*f'(x), so v'(1) = g'(f(1))*f'(1) = g'(2)*f'(1), which doesn't exist since g'(2) doesn't exist. c) w'(x) = g'(g(x))*g'(x), so w'(1) = g'(g(1))*g'(1) = g'(3)*g'(1), which exists since both of them exist.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.