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Value of y' - y'' at a point after simplifying y

This type of question, asked 2 times: 25 Jan 2023, 29 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    25 Jan 2023

    76
    Let y(x)=(1+x)(1+x2)(1+x4)(1+x8)(1+x16)y(x) = (1 + x)\left( 1 +x^{2} \right)\left( 1 +x^{4} \right)\left( 1 +x^{8} \right)\left( 1 +x^{16} \right). Then y′−y′′y^{'}-y^{''} at x=−1x = - 1 is equal to :

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  2. Question 2

    29 Jan 2024

    167
    Let y=log⁡e(1−x21+x2),−1<x<1y =\log_{e}\left( \frac{1 -x^{2}}{1 +x^{2}} \right), - 1 < x < 1. Then at x=12x =\frac{1}{2}, the value of 225(y′−y′′)225\left( y^{'}-y^{''} \right) is equal to

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