Question

If $f\left(x\right)=\left(x - 1\right)\left(x - 2\right)\left(x - 3\right)\left(x - 4\right)\left(x - 5\right)$ , then the value of $\left(\text{f}\right)^{'} \left(5\right)$ is equal to

• A. $0$
• B. $120$
• C. $24$
• D. $5$

Answer 1

Answer: (C)

$f^{\prime}(x)=(x-2)(x-3)(x-4)(x-5)+(x-1)(x-3)(x-4)(x-5)$ $+\ldots+(x-1)(x-2)(x-3)(x-4)$
Putting $x=5$, we get,
$f^{\prime}(5)=0+0+0+0+(5-1)(5-2)(5-3)(5-4)$
$f^{\prime}(5)=24$