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Câu hỏi: Cho hàm số $f\left( x \right)=\ln \left( {{x}^{2}}+1 \right)$. Giá trị ${f}'\left( 2 \right)$ bằng
A. $2$.
B. $\dfrac{4}{5}$.
C. $\dfrac{4}{2\ln 5}$.
D. $\dfrac{4}{3\ln 2}$.
A. $2$.
B. $\dfrac{4}{5}$.
C. $\dfrac{4}{2\ln 5}$.
D. $\dfrac{4}{3\ln 2}$.
Ta có $f\left( x \right)=\ln \left( {{x}^{2}}+1 \right)$ $\Rightarrow {f}'\left( x \right)=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{\prime }}}{{{x}^{2}}+1}=\dfrac{2x}{{{x}^{2}}+1}$ $\Rightarrow {f}'\left( 2 \right)=\dfrac{2.2}{{{2}^{2}}+1}=\dfrac{4}{5}$.
Đáp án B.