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Questions  >>  EAMCET  >>  Mathematics
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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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A)
y=(1+x)(1+xx).............(1+x^2n) take log lny=ln(1+x) +ln(1+xx).....ln(1+x^2n) (1/y)dy/dx=1/(1+x) +2x/(1+xx)....2nx^2n-1/(1+x^2n) At x=o y=1 put values we have dy/dx=1 ans
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