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