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The derivative of y = (1-x) (2-x)…(n-x) ...

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

A

`0`

B

`(-1)(n-1)!`

C

`n!-1`

D

`(-1)^(n-1)(n-1)!`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dy)/(dx)=[(2-x)(3-x)…(n-x)+(1-x)(3-x)…….`
`(n-x)……_(1-x)(2-x)…..(n-1-x)]`
At `x=1, (dy)/(dx)=-[(n-1)!+0+0+…….+0]`
`(dy)/(dx)=(-1)(n-1)!`
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