Cho hàm số f(x) = ( x - 1 )( x - 2 )( x - 3 )...( x - 2019 ). Tính f '(1)

* Hướng dẫn giải

Ta có 

$$\begin{gathered} \underset{x\to 1}{\lim }\frac{f\left(x\right)-f\left(1\right)}{x-1} \\ =\underset{x\to 1}{\lim }\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)...\left(x-2019\right)}{x-1} \\ =\underset{x\to 1}{\lim }\left(x-1\right)\left(x-2\right)\left(x-3\right)...\left(x-2019\right) \\ =\left(-1\right).\left(-2\right).\left(-3\right)....\left(-2018\right)=2018! \end{gathered}$$

Đáp án C