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Câu hỏi: Cho hàm số $y={{10}^{\dfrac{x-1}{x+1}}}.$ Mệnh đề nào dưới đây là đúng?
A. $\dfrac{{{y}'}}{y}=-\dfrac{2\ln 10}{{{\left( x+1 \right)}^{2}}}.$
B. $\dfrac{{{y}'}}{y}=\dfrac{2\ln 10}{{{\left( x+1 \right)}^{2}}}.$
C. $\dfrac{{{y}'}}{y}=\dfrac{x-1}{10\left( x+1 \right)}.$
D. $\dfrac{{{y}'}}{y}=\dfrac{\left( x-1 \right)\ln 10}{10\left( x+1 \right)}.$
A. $\dfrac{{{y}'}}{y}=-\dfrac{2\ln 10}{{{\left( x+1 \right)}^{2}}}.$
B. $\dfrac{{{y}'}}{y}=\dfrac{2\ln 10}{{{\left( x+1 \right)}^{2}}}.$
C. $\dfrac{{{y}'}}{y}=\dfrac{x-1}{10\left( x+1 \right)}.$
D. $\dfrac{{{y}'}}{y}=\dfrac{\left( x-1 \right)\ln 10}{10\left( x+1 \right)}.$
Ta có $y={{10}^{\dfrac{x-1}{x+1}}}\Rightarrow {y}'={{10}^{\dfrac{x-1}{x+1}}}.{{\left( \dfrac{x-1}{x+1} \right)}^{\prime }}.\ln 10=y.\dfrac{2}{{{\left( x+1 \right)}^{2}}}.\ln 10\Rightarrow \dfrac{{{y}'}}{y}=\dfrac{2\ln 10}{{{\left( x+1 \right)}^{2}}}.$ Chọn B.
Đáp án B.