\(f(x) = cos^{4} (4 - 3x)\)
(derivative of cos(x) is -sin(x))
\(f(x) = (cos(4-3x))^{4}\) [cos²x is same as (cosx)²]
f'(x) = 4(cos(4-3x))³ (-sin(4-3x)) (-3)
f'(x) = -12 (cos(4-3x))³(-sin(4-3x))
f'(x) = 12 cos³(4-3x) sin(4-3x)
Thus, c is the correct answer.
