Find the differential of the function y=xcos (8x)

Cos (8x) - 8x*sin (8x). We use the product rule and power rule in this problem. The differential of a function y=f*g is f'*g+f*g', where the ’ symbol of a function means its differential. In our case, the differential of x is just 1, and the differential of cos (8x) is - 8sin (8x) according to the power rule. Therefore, the differential of y is 1*cos (8x) + x * (-8sin (8x)).