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

The derivative of `y=(1-x)(2-x)..........(n-x)` at `x=1` is equal to

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]=(-1)(n-1)!`
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CENGAGE-DIFFERENTIATION-Exercise (Single)
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  14. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

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  19. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

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