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f(x) = sin^-1(2 log x/(1 + (log x)^2)): find f' at a point

The same question, asked 2 times: 11 May 2023 S1*, 12 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2023 S1

    107
    If y=sin⁡−1(log⁡x21+(log⁡x)2)y = \sin^{-1}\left(\frac{\log x^2}{1+(\log x)^2}\right), then dydx∣x=1=\left.\frac{dy}{dx}\right|_{x=1} =

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  2. Question 2

    12 May 2024 S2

    108
    If f(x)=sin⁡−1 ⁣(2log⁡x1+(log⁡x)2)f(x) = \sin^{-1}\!\left(\frac{2\log x}{1+(\log x)^2}\right), then f′(e)f'(e) is

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