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Câu hỏi: Cho hàm số $y=\dfrac{1}{x+1+\ln x}.$ Khi đó $-\dfrac{{{y}'}}{{{y}^{2}}}$ bằng
A. $1+\dfrac{1}{x}.$
B. $\dfrac{x}{x+1}.$
C. $\dfrac{x}{1+x+\ln x}.$
D. $\dfrac{x+1}{1+x+\ln x}.$
A. $1+\dfrac{1}{x}.$
B. $\dfrac{x}{x+1}.$
C. $\dfrac{x}{1+x+\ln x}.$
D. $\dfrac{x+1}{1+x+\ln x}.$
Ta có ${y}'=-\dfrac{1}{{{\left( x+1+\ln x \right)}^{2}}}.\left( 1+\dfrac{1}{x} \right)=-{{y}^{2}}\left( 1+\dfrac{1}{x} \right)\Rightarrow -\dfrac{{{y}'}}{{{y}^{2}}}=1+\dfrac{1}{x}.$
Đáp án A.