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Question

If y=(1+x)(1+x2)(1+x4).....(1+x2n), find dydx at x=0

A
2n
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B
0
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C
1
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D
2n
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Solution

The correct option is B 1
y=(1x)(1+x)(1+x2)...(1+x2n+1)1x=1x2n+11x
dydx=2n+1.x2n+11.(1x)+1x2n+1(1x)2
for x=0,dydx=2n+1.0.1+1012=1

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