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Câu hỏi: Hàm số $y={{\log }_{16}}\left( {{x}^{4}}+16 \right)$ có đạo hàm là :
A. $y'=\dfrac{{{x}^{3}}}{\ln 2}$.
B. $\dfrac{1}{\left( {{x}^{4}}+16 \right).\ln 2}$.
C. $\dfrac{16{{x}^{3}}\ln 2}{{{x}^{4}}+16}$.
D. $\dfrac{{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 2}$.
Ta có : $y={{\log }_{16}}\left( {{x}^{4}}+16 \right)\Rightarrow y'=\dfrac{4{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 16}=\dfrac{{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 2}$.
A. $y'=\dfrac{{{x}^{3}}}{\ln 2}$.
B. $\dfrac{1}{\left( {{x}^{4}}+16 \right).\ln 2}$.
C. $\dfrac{16{{x}^{3}}\ln 2}{{{x}^{4}}+16}$.
D. $\dfrac{{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 2}$.
Ta có : $y={{\log }_{16}}\left( {{x}^{4}}+16 \right)\Rightarrow y'=\dfrac{4{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 16}=\dfrac{{{x}^{3}}}{\left( {{x}^{4}}+16 \right).\ln 2}$.
Đáp án D.