Cho hàm số f (x) = x-2 / x-1 . Tính f'(x)

2/22

Cho hàm số \(f\left( x \right) = \frac{{x - 2}}{{x - 1}}\). Tính \(f'\left( x \right)\)?

\(f'\left( x \right) = \frac{1}{{{{\left( {x - 1} \right)}^2}}}\).

\(f'\left( x \right) = \frac{2}{{{{\left( {x - 1} \right)}^2}}}\).

\(f'\left( x \right) = \frac{{ - 2}}{{{{\left( {x - 1} \right)}^2}}}\).

\(f'\left( x \right) = \frac{{ - 1}}{{{{\left( {x - 1} \right)}^2}}}\)

Giải thích

Ta có \(f'\left( x \right) = \frac{{{{\left( {x - 2} \right)}^\prime }.\left( {x - 1} \right) - \left( {x - 2} \right).{{\left( {x - 1} \right)}^\prime }}}{{{{\left( {x - 1} \right)}^2}}} = \frac{{x - 1 - \left( {x - 2} \right)}}{{{{\left( {x - 1} \right)}^2}}} = \frac{1}{{{{\left( {x - 1} \right)}^2}}}\).