A) 0
B) \[(-1)\,(n-1)\,!\]
C) \[n!\,-\,1\]
D) \[{{(-1)}^{n-1}}(n-1)\,!\]
E) \[{{(-1)}^{n}}\,(n-1)\,!\]
Correct Answer: B
Solution :
\[\frac{dy}{dx}=-[(2-x)(3-x).....(n-x)+(1-x)(3-x)....(n-x)\] \[+.....(1-x)(2-x).....(n-1-x)]\]at \[x=1\] \[\frac{dy}{dx}=-[(n-1)!+0+.......+0]\]\[=(-1)n-1\ !\]
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