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Câu hỏi: Cho hàm số $y=f(x)=\sqrt[3]{\cos 2 x}$. Tìm mệnh đề đúng.
A. $3 f(x) \cdot f^{\prime}(x)+2 \sin 2 x=0$.
B. $f^{\prime}\left(\dfrac{\pi}{2}\right)=0$.
C. $f^{\prime}\left(\dfrac{\pi}{2}\right)=1$.
D. $f^{\prime}(x)=\dfrac{-2 \sin 2 x}{3 \sqrt[3]{\cos 2 x}}$.
A. $3 f(x) \cdot f^{\prime}(x)+2 \sin 2 x=0$.
B. $f^{\prime}\left(\dfrac{\pi}{2}\right)=0$.
C. $f^{\prime}\left(\dfrac{\pi}{2}\right)=1$.
D. $f^{\prime}(x)=\dfrac{-2 \sin 2 x}{3 \sqrt[3]{\cos 2 x}}$.
Ta có: $y^{\prime}=f^{\prime}(x)=-\dfrac{2 \sin 2 x}{3 \sqrt[3]{\cos ^2 2 x}} \Rightarrow f^{\prime}\left(\dfrac{\pi}{2}\right)=\dfrac{-2 \sin \pi}{3 \sqrt[3]{\cos ^2 \pi}}=0$.
Đáp án B.