If f and g are the functions whose graphs are shown, letu(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)&nbsp;&nbsp;&nbsp;&nbsp;u'(1) =&nbsp;It does exist.u'(1) does not exist because f '(1) does not exist.&nbsp;&nbsp;&nbsp;&nbsp; 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)&nbsp;&nbsp;&nbsp;&nbsp;v'(1) =&nbsp;It does exist.v'(1) does not exist because f '(1) does not exist.&nbsp;&nbsp;&nbsp;&nbsp; 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)&nbsp;&nbsp;&nbsp;&nbsp;w'(1) =&nbsp;It does exist.w'(1) does not exist because f '(1) does not exist.&nbsp;&nbsp;&nbsp;&nbsp; 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.&nbsp;&nbsp;&nbsp;

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If f and g are the functions whose graphs are shown, letu(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)&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;u&#039;(1) =&amp;nbsp;It does exist.u&#039;(1) does not exist because f &#039;(1) does not exist.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; u&#039;(1) does not exist because g&#039;(1) does not exist.u&#039;(1) does not exist because f &#039;(3) does not exist.u&#039;(1) does not exist because g&#039;(2) does not exist.(b)&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;v&#039;(1) =&amp;nbsp;It does exist.v&#039;(1) does not exist because f &#039;(1) does not exist.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&#039;(1) does not exist because g&#039;(1) does not exist.v&#039;(1) does not exist because f &#039;(3) does not exist.v&#039;(1) does not exist because g&#039;(2) does not exist.(c)&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;w&#039;(1) =&amp;nbsp;It does exist.w&#039;(1) does not exist because f &#039;(1) does not exist.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; w&#039;(1) does not exist because g&#039;(1) does not exist.w&#039;(1) does not exist because f &#039;(3) does not exist.w&#039;(1) does not exist because g&#039;(2) does not exist.&amp;nbsp;&amp;nbsp;&amp;nbsp;

If f and g are the functions whose

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