WBJEE · Maths · Differentiation
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 \(\left(\frac{d y}{d x}\right)\) at \(x=0\) is
- A 0
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Given, \(y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right)+\ldots+\left(1+x^{2 n}\right)\) \(\Rightarrow \log y=\log (1+x)+\log \left(1+x^{2}\right)\) \(+\log \left(1+x^{4}\right)+\ldots+\log \left(1+x^{2n}\right)\)…
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