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Question

If y=(x2−1)m, then the value of (2m)th differential coefficient of y is

A
m
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B
(2m)!
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C
2m
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D
m!
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Solution

The correct option is B (2m)!
Expanding binomially, we get
y=(x21)m=mC0 x2m+mC1 x2m1(1)+.....
On differentiating, all the terms, except first, reduces to zero. Therefore,
d2mdx2m(x21)m=mC0 2m(2m1)(2m2).....1=(2m)!

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