Determine the coefficient of x4x^4x4 in the Taylor expansion of f(x)=e2xf(x) = e^{2x}f(x)=e2x centered at a=1a = 1a=1.
22e24!\frac{2^2 e^2}{4!}4!22e2
24e24!\frac{2^4 e^2}{4!}4!24e2
24e4!\frac{2^4 e}{4!}4!24e
e24!\frac{e^2}{4!}4!e2