Q94 / 160 · WBJEE 2010 · Mathematics

If $y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots\left(1+x^{2 n}\right)$ then the value of $\left(\frac{d y}{d x}\right)_{x=0}$ is

  • A
    0
  • B
    -1
  • Correct answer
    C
    1
  • D
    2

Solution

Hints: T-log \& Differentiate $$ \begin{aligned} & \frac{d y}{d x}=y\left[\frac{1}{1+x}+\frac{2 x}{1+x^2}+\ldots\right] \text { Put } x=0 \\ & \frac{d y}{d x}=1 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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