If `y=(1+x)(1+x^2)(1+x^4)(1+x^8)...........(1+x^n)`,find `dy//dx`

Explanation

To find the derivative \( \frac{dy}{dx} \) of the function

\[ y = (1+x)(1+x^2)(1+x^4)(1+x^8)\cdots(1+x^n), \]

we can use logarithmic differentiation to simplify the process. Here’s a step-by-step solution:

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