QCM 1
Le nombre dérivé \(f′(−3)\) de la fonction \(f\) définie sur \(\mathbf{R}\)\ {0.5} par \(f(x) =\frac{x−3}{2x−1}\) est:
Votre choixChoix attenduRéponse
\(f'(x) =(\frac{u}{v})'\)
où
\(\begin{cases}u=x-3\\v=2x-1\end{cases}\)
\(\iff \begin{cases}u'=1\\v'=2\end{cases}\)
\(f'(x) =\frac{u'v-uv'}{v^2}=\frac{1(2x-1)-(x-3) \times 2}{(2x-1)^2}\)
\(\iff f'(x) =\frac{u'v-uv'}{v^2}=\frac{2x-1-(2x-6)}{(2x-1)^2}\)
\(\iff f'(x) =\frac{2x-1-2x+6}{v^2}{(2x-1)^2}\)
\(\iff f'(x) =\frac{5}{(2x-1)^2}\)
donc \(f'(-3) =\frac{5}{(2 \times (-3)-1)^2}\)
\(\iff f'(-3) =\frac{5}{(-6-1)^2}\)
\(\iff f'(-3) =\frac{5}{(-7)^2}\)
\(\iff f'(-3) =\frac{5}{49}\)