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