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Câu hỏi: Cho hàm số $y=co{{s}^{2}}x$. Khi đó ${{y}^{(3)}}\left( \dfrac{\pi }{3} \right)$ bằng
A. -2
B. 2
C. $2\sqrt{3}$
D. - $2\sqrt{3}$
A. -2
B. 2
C. $2\sqrt{3}$
D. - $2\sqrt{3}$
Ta có ${y}'=2\cos x.\left( -\sin x \right)=-\sin 2x;{{y}'}'=-2cos2x;$
${{y}^{(3)}}=-2\left( -2\sin 2x \right)=4\sin 2x\Rightarrow {{y}^{(3)}}\left( \dfrac{\pi }{3} \right)=4\sin \left( \dfrac{2\pi }{3} \right)=2\sqrt{3}$
${{y}^{(3)}}=-2\left( -2\sin 2x \right)=4\sin 2x\Rightarrow {{y}^{(3)}}\left( \dfrac{\pi }{3} \right)=4\sin \left( \dfrac{2\pi }{3} \right)=2\sqrt{3}$
Đáp án C.