Verified answer

1)  y = CosxCos7x - SinxSin7x = Cos(x + 7x) = Cos8x

y' = (Cos8x)' = - Sin8x * (8x)' = - 8Sin8x

2) y = CosxCos7x + SinxSin7x = Cos(x - 7x) = Cos(- 6x) = Cos6x

y' = (Cos6x)' = - Sin6x * (6x)' = - 6Sin6x

3) y = Sin7xCosx - SinxCos7x = Sin(7x - x) = Sin6x

y' = (Sin6x)' = Cos6x * (6x)' = 6Cos6x

4) y = Sin7xCosx + SinxCos7x = Sin(7x + x) = Sin8x

y' = (Sin8x)' = Cos8x * (8x)' = 8Cos8x