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Question

If y=(1+x)(1+x2)(1+x4)(1+x2n) then dydx at x = 0 is

A
-1
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B
1
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C
None of these
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Solution

The correct option is B 1
Since, y=(1+x)(1+x2)(1+x4)(1+x2n),(1x)y=(1x2)(1+x2)(1+x4)(1+x2n)=(1x4)(1+x4)(1+x2n+1)y=1x2n+1(1x)dydx=(1x)(2n+1.x2n)(1x2n+1)(1)(1x)2dydxx=0=(1)(0)(1)(1)(1)2=1

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