What is the derivative of the function y=2cos(3x-1)*sin(3x-1)?

We recognize the formula of the double angle in the given
expresison of the function:

y = 2 sin (3x-1)*cos (3x -
1)

y = sin 2*(3x-1)

y = sin
(6x - 2)

Since the function to be differentiated is the
result of composition of two functions, we'll use the chain rule to detemrine the first
derivative of the function.

We'll differentiate with
respect to x:

dy/dx = [cos (6x - 2)]*(6x -
2)'

dy/dx = 6*cos(6x -
2)

The first derivative of the given function
is: dy/dx = 6*cos(6x - 2).