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Question: Answered & Verified by Expert
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
MathematicsDifferentiationWBJEEWBJEE 2010
Options:
  • A 0
  • B -1
  • C 1
  • D 2
Solution:
1506 Upvotes Verified Answer
The correct answer is: 1
Hints: T-log \& Differentiate
$$
\begin{aligned}
& \frac{d y}{d x}=y\left[\frac{1}{1+x}+\frac{2 x}{1+x^2}+\ldots\right] \text { Put } x=0 \\
& \frac{d y}{d x}=1
\end{aligned}
$$

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