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If $y=(1+x)(1+x^2)(1+x^4)........(1+x^{2^{n}}),$ then $\bigg(\large\frac{dy}{dx}\bigg)_{x =0}=$

\[(a)\;0 \quad (b)\;\frac{1}{2} \quad (c)\;1 \quad (d)\;2\]

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