d/dx sin2x = cos2x * (2x)' = 2cos2x
d/dx (1-2cos²3x) = -2 * (cos²3x)' = -2 * 2cos3x * (cos3x)'
= -4cos3x * (-sin3x) * (3x)'
= 4sin3xcos3x * 3
= 12sin3xcos3x
d/dx -2sin2x (1-2cos²3x)
= -2[(1-2cos²3x)(sin2x)' + (sin2x)(1-2cos²3x)']
= -2[(1-2cos²3x)(2cos2x) + (sin2x)(12sin3xcos3x)]
= -2(-2cos2xcos6x + 6sin2xsin6x)
= 4(cos2xcos6x - 3sin2xsin6x)
= 4(cos2xcos6x - sin2xsin6x - 2sin2xsin6x)
= 4[cos8x - 2*(-1/2)(cos(2x+6x) - cos(2x-6x))]
= 4(cos8x + cos8x - cos4x)
= 4(2cos8x - cos4x)
= 8cos(8x) - 4cos(4x)