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Câu hỏi: Đạo hàm của hàm số $y=\dfrac{1}{x \sqrt[4]{x}}$ là
A. $y^{\prime}=-\dfrac{5}{4 \sqrt[4]{x^9}}$.
B. $y^{\prime}=\dfrac{5}{4} \sqrt[4]{x}$.
C. $y^{\prime}=\dfrac{1}{x^{2 \sqrt[4]{x}}}$.
D. $y^{\prime}=\dfrac{1}{4 \sqrt[4]{x^5}}$.
A. $y^{\prime}=-\dfrac{5}{4 \sqrt[4]{x^9}}$.
B. $y^{\prime}=\dfrac{5}{4} \sqrt[4]{x}$.
C. $y^{\prime}=\dfrac{1}{x^{2 \sqrt[4]{x}}}$.
D. $y^{\prime}=\dfrac{1}{4 \sqrt[4]{x^5}}$.
TXĐ: $D=(0 ;+\infty)$
Ta có: $y=\dfrac{1}{x x^{\dfrac{1}{4}}}=\dfrac{1}{x^{\dfrac{5}{4}}}=x^{-\dfrac{5}{4}}$.
$\Rightarrow y^{\prime}=\left(x^{-\dfrac{5}{4}}\right)^{\prime}=-\dfrac{5}{4} x^{-\dfrac{9}{4}}=-\dfrac{5}{4 \sqrt[4]{x^9}}$.
Ta có: $y=\dfrac{1}{x x^{\dfrac{1}{4}}}=\dfrac{1}{x^{\dfrac{5}{4}}}=x^{-\dfrac{5}{4}}$.
$\Rightarrow y^{\prime}=\left(x^{-\dfrac{5}{4}}\right)^{\prime}=-\dfrac{5}{4} x^{-\dfrac{9}{4}}=-\dfrac{5}{4 \sqrt[4]{x^9}}$.
Đáp án A.