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Câu hỏi: Cho hàm số $f\left( x \right)={{\log }_{2}}\left( 1+{{2}^{x}} \right)$. Tính giá trị $S={f}'\left( 0 \right)+{f}'\left( 1 \right)$.
A. $S=\dfrac{7}{6}$
B. $S=\dfrac{7}{5}$
C. $S=\dfrac{6}{5}$
D. $S=\dfrac{7}{8}$
A. $S=\dfrac{7}{6}$
B. $S=\dfrac{7}{5}$
C. $S=\dfrac{6}{5}$
D. $S=\dfrac{7}{8}$
${f}'\left( x \right)=\dfrac{{{\left( 1+{{2}^{x}} \right)}^{\prime }}}{\left( 1+{{2}^{x}} \right)\ln 2}=\dfrac{{{2}^{x}}\ln 2}{\left( 1+{{2}^{x}} \right)\ln 2}=\dfrac{{{2}^{x}}}{1+{{2}^{x}}}\Rightarrow \left\{ \begin{aligned}
& {f}'\left( 0 \right)=\dfrac{1}{2} \\
& {f}'\left( 1 \right)=\dfrac{2}{3} \\
\end{aligned} \right.\Rightarrow S=\dfrac{7}{6}$.
& {f}'\left( 0 \right)=\dfrac{1}{2} \\
& {f}'\left( 1 \right)=\dfrac{2}{3} \\
\end{aligned} \right.\Rightarrow S=\dfrac{7}{6}$.
Đáp án A.