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Derivative of tan^-1((sqrt(1 + x^2) - 1)/x) with respect to sin^-1(2x/(1 + x^2))

The same question, asked 2 times: May 2021 S1, 11 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    May 2021 S1

    141
    Derivative of tan⁡−1 ⁣1+x2−1x\tan^{-1}\!\frac{\sqrt{1+x^2}-1}{x} w.r.t. sin⁡−1 ⁣2x1+x2\sin^{-1}\!\frac{2x}{1+x^2} is

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  2. Question 2

    11 Apr 2026 S2

    70
    The derivative of tan⁡−1(1+x2−1x)\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right) with respect to sin⁡−1(2x1+x2)\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) is...

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