Suppose $$f(x) = \ln\left( \frac{e x^{6}}{(x-3)^{3}} \right).$$
(a) Find $f'( x ) =$ . (Hint: Apply the laws of logarithms to $f(x)$ before taking its derivative.)
(b) Find $\frac{d}{dx} \left( e^{f(x)} \right) =$ .