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),(1−x)y=(1−x2)(1+x2)(1+x4)⋯(1+x2n)=(1−x4)(1+x4)⋯(1+x2n+1)∴y=1−x2n+1(1−x)∵dydx=(1−x)(−2n+1.x2n)−(1−x2n+1)(−1)(1−x)2∴dydx∣∣x=0=(1)(0)−(1)(−1)(1)2=1