Google
Câu hỏi: Hàm số $f\left( x \right)={{\log }_{2}}\left| x-1 \right|$ có đạo hàm là
A. $\dfrac{1}{\left( x-1 \right)\ln 2}$.
B. $\dfrac{-1}{\left( x-1 \right)\ln 2}$
C. $\dfrac{1}{\left| x-1 \right|\ln 2}$.
D. $\dfrac{-1}{\left| x-1 \right|\ln 2}$.
A. $\dfrac{1}{\left( x-1 \right)\ln 2}$.
B. $\dfrac{-1}{\left( x-1 \right)\ln 2}$
C. $\dfrac{1}{\left| x-1 \right|\ln 2}$.
D. $\dfrac{-1}{\left| x-1 \right|\ln 2}$.
Ta có ${f}'\left( x \right)={{\left( {{\log }_{2}}\left| x-1 \right| \right)}^{\prime }}=\dfrac{{{\left| x-1 \right|}^{\prime }}}{\left| x-1 \right|\ln 2}=\dfrac{{{\left( x-1 \right)}^{\prime }}.\left( x-1 \right)}{\left| x-1 \right|.\left| x-1 \right|.\ln 2}=\dfrac{1}{\left( x-1 \right)\ln 2}$
Đáp án A.