F and G Are Functions Whose Graphs Are Shown Below $F ( x ) = f ( g ( x ) ) , G ( x ) = g ( f ( x ) )$

Essay

f and g are functions whose graphs are shown below. Let $F ( x ) = f ( g ( x ) ) , G ( x ) = g ( f ( x ) )$ and $H ( x ) = f ( f ( x ) )$ Find each derivative, if it exists. If it does not exist, explain. (a) $F ^ { \prime } ( 2 )$ (b) $F ^ { \prime } ( 6 )$ (c) $F ^ { \prime } ( 8 )$ (d) $G ^ { \prime } ( 2 )$ (e) $G ^ { \prime } ( 4 )$ (f) $G ^ { \prime } ( 10 )$ (g) $H ^ { \prime } ( 4 )$ (h) $H ^ { \prime } ( 6 )$ (i) $H ^ { \prime } ( 10 )$