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Câu hỏi: Hàm số $y={{\left( 3-{{x}^{2}} \right)}^{-\dfrac{4}{3}}}$ có đạo hàm trên khoảng $\left( -\sqrt{3};\sqrt{3} \right)$ là:
A. $y=\dfrac{8}{3}x{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
B. $y=-\dfrac{8}{3}x{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
C. $y=-\dfrac{4}{3}{{x}^{2}}{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
D. $y=-\dfrac{4}{3}{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
A. $y=\dfrac{8}{3}x{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
B. $y=-\dfrac{8}{3}x{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
C. $y=-\dfrac{4}{3}{{x}^{2}}{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
D. $y=-\dfrac{4}{3}{{\left( 3-{{x}^{2}} \right)}^{\dfrac{-7}{3}}}$.
Phân tích: $y^{\prime}=-\dfrac{4}{3} \cdot(-2 x) \cdot\left(3-x^2\right)^{\dfrac{-7}{3}}=\dfrac{8}{3} x\left(3-x^2\right)^{\dfrac{-7}{3}}$.
Đáp án A.