Question

See attached graph
If f and g are 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'(1)
b.)v'(1)
c.)w'(1)

Answer 1

Use the chain rule: \[
(f(g(x))' = f'(g(x)) \cdot g'(x)
\]