Differentiation Question 362
Question: If $ y={{(x^{2}-1)}^{m}} $ , then the $ {{(2m)}^{th}} $ differential coefficient of y is
[MP PET 1987]
Options:
A) m
B) $ (2m)! $
C) 2m
D) m!
Show Answer
Answer:
Correct Answer: B
Solution:
Expanding binomially $ y={{(x^{2}-1)}^{m}}{{=}^{m}}C _{o}x^{2m}{{+}^{m}}C_1{x^{2m-2}}(-1)+……. $
So on differentiating all the terms except first reduces to zero, therefore $ \frac{d^{2m}y}{dx^{2m}}{{=}^{m}}C_02m(2m-1)(2m-2)….1=(2m)! $ .
BETA
