\text { Use logarithmic differentiation to find the derivative of } f(x)=x^{\cos 2 x} \text {. } f^{\prime}(x)=x^{\operatorname{con} 2 x}\left[\frac{\cos 2 x}{x}-2(\sin 2 x) \ln x\right] f^{\prime}(x)=(-2 \sin 2 x) x^{\cos 2 x} f^{\prime}(x)=(-2 \sin 2 x) x^{\cos 2 x} f^{\prime}(x)=(\cos 2 x) x^{\cos 2 x-1} f^{\prime}(x)=x^{\cos 2 x}(\ln x-2 \sin 2 x)