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.u'(1) does not exist because f '(1) does not exist.    u'(1) does not exist because g'(1) does not exist.u'(1) does not exist because f '(3) does not exist.u'(1) does not exist because g'(2) does not exist.(b)    v'(1) = It does exist.v'(1) does not exist because f '(1) does not exist.    v'(1) does not exist because g'(1) does not exist.v'(1) does not exist because f '(3) does not exist.v'(1) does not exist because g'(2) does not exist.(c)    w'(1) = Your answer cannot be understood or graded. More InformationIt does exist.w'(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 '(3) does not exist.w'(1) does not exist because g'(2) does not exist.

I'm sorry, but your question seems to be incomplete. Could you please provide the graphs of the functions f and g? Without these, it's impossible to determine the derivatives of the composite functions u(x), v(x), and w(x).

However, I can explain how to find these derivatives if the graphs were provided:

(a) To find u'(1), you would use the chain rule for derivatives, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, times the derivative of the inner function. So, u'(1) = f'(g(1)) * g'(1). If either f'(g(1)) or g'(1) does not exist, then u'(1) does not exist.

(b) Similarly, to find v'(1), you would use the chain rule again: v'(1) = g'(f(1)) * f'(1). If either g'(f(1)) or f'(1) does not exist, then v'(1) does not exist.

(c) For w'(1), you would use the chain rule once more: w'(1) = g'(g(1)) * g'(1). If either g'(g(1)) or g'(1) does not exist, then w'(1) does not exist.

Please provide the graphs of f and g so I can give a more specific answer.