Problem 65E

65. 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.

(a) $u^{\prime}(1)$

(b) $v^{\prime}(1)$

(c) $w^{\prime}(1)$

Step-by-Step Solution