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Câu hỏi: Cho hàm số $y=f\left( x \right)={{\log }_{2}}\left( 1+{{2}^{x}} \right)$. Giá trị $S=f'\left( 0 \right)+f'\left( 1 \right)$ bằng
A. $\dfrac{6}{5}$
B. $\dfrac{7}{8}$
C. $\dfrac{7}{6}$
D. $\dfrac{7}{5}$
A. $\dfrac{6}{5}$
B. $\dfrac{7}{8}$
C. $\dfrac{7}{6}$
D. $\dfrac{7}{5}$
Ta có $f'\left( x \right)=\dfrac{{{\left( 1+{{2}^{x}} \right)}^{'}}}{\left( 1+{{2}^{x}} \right).\ln 2}=\dfrac{{{2}^{x}}}{1+{{2}^{x}}}\Rightarrow S=f'\left( 0 \right)+f'\left( 1 \right)=\dfrac{1}{2}+\dfrac{2}{3}=\dfrac{7}{6}$
Đáp án C.