What is the value of the 16th order derivative $f ^ { ( 16 ) } ( x )$ of the function $f ( x ) = e ^ { x } \cdot \cos x$ at the point $x = 0$?
A) 32 B) 64 C) 128 D) 256 E) 512

Let $a$ and $b$ be real numbers. A function $f$ is defined on the set of positive real numbers as
$$f ( x ) = a x ^ { a } + b x ^ { b }$$
$$\begin{aligned} & f ( 1 ) = 6 \\ & f ^ { \prime } ( 1 ) = 20 \end{aligned}$$
Given that, what is $f''(1)$?
A) 44
B) 46
C) 48
D) 50
E) 52