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Derivative of f(sec x) with respect to g(tan x), or the other way round, at x = pi/4 given f' and g' values

The same question, asked 2 times: 9 May 2024 S1*, 12 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    9 May 2024 S1

    105
    The derivative of f(sec⁡x)f(\sec x) with respect to g(tan⁡x)g(\tan x) at x=π4x=\frac{\pi}{4}, where f′(2)=4f'(\sqrt{2})=4 and g′(1)=2g'(1)=2, is

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  2. Question 2

    12 May 2024 S1

    109
    The derivative of f(tan⁡x)f(\tan x) w.r.t. g(sec⁡x)g(\sec x) at x=π4x=\frac{\pi}{4}, where f′(1)=2f'(1)=2 and g′(2)=4g'(\sqrt{2})=4, is

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