Determine the derivative of fx cos2 x43 6 cos2 x42 sin2 x4

Determine the derivative of: f(x) = (cos(2 x-4))^3 -6 (cos(2 x-4)^2) sin(2 x-4) -6 (cos(2 x-4))^2 sin(2 x-4) -18 (cos(2 x-4))^2 sin(2 x-4) -18 (cos(2 x-4))^2 Not listed -6 (cos(2 x-4))^2

Solution

using chain rule

f’(x) = d/dx (cos(2x -4))^3

= 3 (cos(2x-4))^2 * d/dx cos(2x-4)

= 3(cos(2x-4))^2 * -sin(2x-4) * d/dx 2x

= 3(cos(2x-4))^2 * -sin(2x-4) * 2

= -6 (cos(2x-4))^2 * -sin(2x-4)