Search any question & find its solution
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
Options:
Solution:
1506 Upvotes
Verified Answer
The correct answer is:
1
Hints: T-log \& Differentiate
$$
\begin{aligned}
& \frac{d y}{d x}=y\left[\frac{1}{1+x}+\frac{2 x}{1+x^2}+\ldots\right] \text { Put } x=0 \\
& \frac{d y}{d x}=1
\end{aligned}
$$
$$
\begin{aligned}
& \frac{d y}{d x}=y\left[\frac{1}{1+x}+\frac{2 x}{1+x^2}+\ldots\right] \text { Put } x=0 \\
& \frac{d y}{d x}=1
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.