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Câu hỏi: . Cho hàm số $f\left( x \right)={{\log }_{2}}\left( {{x}^{2}}+1 \right)$, tính ${f}'\left( 1 \right)$.
A. ${f}'\left( 1 \right)=1$
B. ${f}'\left( 1 \right)=\dfrac{1}{2\ln 2}$
C. ${f}'\left( 1 \right)=\dfrac{1}{2}$
D. ${f}'\left( 1 \right)=\dfrac{1}{\ln 2}$
A. ${f}'\left( 1 \right)=1$
B. ${f}'\left( 1 \right)=\dfrac{1}{2\ln 2}$
C. ${f}'\left( 1 \right)=\dfrac{1}{2}$
D. ${f}'\left( 1 \right)=\dfrac{1}{\ln 2}$
Tập xác định: $D=\mathbb{R}$.
${f}'\left( x \right)=\dfrac{2\text{x}}{\left( {{x}^{2}}+1 \right)\ln 2}\Rightarrow {f}'\left( 1 \right)=\dfrac{2.1}{\left( {{1}^{2}}+1 \right)\ln 2}=\dfrac{1}{\ln 2}$.
${f}'\left( x \right)=\dfrac{2\text{x}}{\left( {{x}^{2}}+1 \right)\ln 2}\Rightarrow {f}'\left( 1 \right)=\dfrac{2.1}{\left( {{1}^{2}}+1 \right)\ln 2}=\dfrac{1}{\ln 2}$.
Đáp án D.