Google
Câu hỏi: Hàm số $f\left( x \right)=\ln \dfrac{x+1}{x-1}$ có đạo hàm là
A. $f'\left( x \right)=-\dfrac{2}{{{x}^{2}}+1}.$
B. $f'\left( x \right)=-\dfrac{2}{{{\left( x+1 \right)}^{2}}}.$
C. $f'\left( x \right)=-\dfrac{2}{{{x}^{2}}-1}.$
D. $f'\left( x \right)=-\dfrac{x-1}{x+1}.$
A. $f'\left( x \right)=-\dfrac{2}{{{x}^{2}}+1}.$
B. $f'\left( x \right)=-\dfrac{2}{{{\left( x+1 \right)}^{2}}}.$
C. $f'\left( x \right)=-\dfrac{2}{{{x}^{2}}-1}.$
D. $f'\left( x \right)=-\dfrac{x-1}{x+1}.$
$f'\left( x \right)={{\left( \dfrac{x+1}{x-1} \right)}^{\prime }}\left( \dfrac{x-1}{x+1} \right)=\dfrac{-2}{{{\left( x-1 \right)}^{2}}}\left( \dfrac{x-1}{x+1} \right)=-\dfrac{2}{{{x}^{2}}-1}.$
Đáp án C.