Cho hàm số \(f \left( x \right)= \frac{1}{2x-1} \). Tính \({{f}'}' \left( -1 \right) \). A.\(-\frac{8}{27}\). B.\(\frac{2}{9}\). C.\(\frac{8}{27}\). D.\(-\frac{4}{27}\).
Đáp án đúng: A Giải chi tiết:Ta có \({f}'\left( x \right)={{\left( \frac{1}{2x-1} \right)}^{\prime }}=\frac{-2}{{{\left( 2x-1 \right)}^{2}}}\) \(\Rightarrow {{f}'}'\left( x \right)={{\left( \frac{-2}{{{\left( 2x-1 \right)}^{2}}} \right)}^{\prime }}=\frac{2.2.2\left( 2x-1 \right)}{{{\left( 2x-1 \right)}^{4}}}=\frac{8}{{{\left( 2x-1 \right)}^{3}}}\) Nên \({{f}'}'\left( -1 \right)=\frac{8}{{{\left( 2.\left( -1 \right)-1 \right)}^{3}}}=-\frac{8}{27}\). Chọn A.