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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)ldots=(1x2n)(1+x2n=1x2n+1
y=1x2n+1(1x)
dydx=(1x)(2n+1.x2n+1)(12n+1)(1)(1x)2
dydx|x=0=(1x)(2n+1.0)(10)(1)(1x)2
=1

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