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$The derivative of y = (1 - x) (2 - x) . . . . (n - x) at x = 1 is$

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$(- 1) (n - 1)!$

$n! - 1$

${(- 1)}^{n - 1} (n - 1)!$

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{dy}{dx} = - [(2 - x) (3 - x) . . . . (n - x) + (1 - x) (3 - x) . . . . (n - x) + . . (1 - x) (2 - x) . . . (n - 1 - x)] \\ At x = 1, \\ \frac{dy}{dx} = - [(n - 1)! + 0 + . . . . + 0] = (- 1) (n - 1)! \end{array}$

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