Question

Let $y (x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$. Then $y^{\prime}-y^{\prime \prime}$ at $x=-1$ is equal to :

• A. 976
• B. 944
• C. 496
• D. 464

Answer 1

Answer: (C)

496

Answer 2

The correct answer is (C) : 496
$y=\frac{1−x^{32}}{1-x​}$
$⇒ y−xy=1−x^{32}$
$y'−xy'−y=−32x^{31 }$
$y''−xy''−y'−y'=−(32)(31)x^{30}$
at x=−1
$⇒ y'−y''=496$