Differentiation Question 340
Question: The derivative of $ y=(1-x)(2-x)….(n-x) $ at $ x=1 $ is equal to
[Kerala (Engg.) 2005]
Options:
A) 0
B) $ (-1)(n-1)! $
C) $ n!-1 $
D) $ {{(-1)}^{n-1}}(n-1)! $
E) $ {{(-1)}^{n}}(n-1)! $
Show Answer
Answer:
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\ ! $
BETA
