The derivative of the given function y = (cos 2x)^x can be obtained by transforming the given expression into its logarithmic form. y = (cos 2x)^x ln y = x ln (cos 2x) dy/y = x * -dx/2 sin 2x + ln (cos 2x) dx dy/dx = -xy/2 sin 2x + ln (cos 2x). This is the final answer
