Ngân hàng bài tập
B
Cho hàm số $f\left(x\right)=\dfrac{x-2}{x-1}$. Tìm $f'\left(x\right)$.
 | $f'\left(x\right)=\dfrac{1}{\left(x-1\right)^2}$ |
 | $f'\left(x\right)=\dfrac{2}{\left(x-1\right)^2}$ |
 | $f'\left(x\right)=\dfrac{-2}{\left(x-1\right)^2}$ |
 | $f'\left(x\right)=\dfrac{-1}{\left(x-1\right)^2}$ |
1 lời giải
Chọn phương án A.
$\begin{aligned}
f'\left(x\right)&=\dfrac{\left(x-2\right)^{\prime }\cdot\left(x-1\right)-\left(x-2\right)\cdot\left(x-1\right)^{\prime}}{\left(x-1\right)^2}\\
&=\dfrac{x-1-\left(x-2\right)}{\left(x-1\right)^2}\\
&=\dfrac{1}{\left(x-1\right)^2}.
\end{aligned}$
$\left(\dfrac{ax+b}{cx+d}\right)^\prime=\dfrac{ad-bc}{(cx+d)^2}$