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Derivative of f(trig x) with respect to g(trig x) at a point, given f' and g' values

This type of question, asked 5 times: 9 May 2024 S1, 12 May 2024 S1, 20 Apr 2026 S1, 15 May 2026 S1, 15 May 2026 S2. All 5 questions 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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  3. Question 3

    20 Apr 2026 S1

    73
    The derivative of f(sin⁡x)f(\sin x) with respect to g(sec⁡x)g(\sec x) at x=π4x = \dfrac{\pi}{4}, given that f′(12)=3f'\left(\dfrac{1}{\sqrt{2}}\right) = 3 and g′(2)=1g'(\sqrt{2}) = 1 is.....

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  4. Question 4

    15 May 2026 S1

    73
    The derivative of f(cos⁡x)f(\cos x) with respect to g(tan⁡x)g(\tan x) at x=π6x = \dfrac{\pi}{6}, given that f′(32)=4f'\left(\dfrac{\sqrt{3}}{2}\right) = 4 and g′(13)=2g'\left(\dfrac{1}{\sqrt{3}}\right) = 2 is:

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  5. Question 5

    15 May 2026 S2

    74
    If f′(12)=3f'\left(\dfrac{1}{2}\right) = \sqrt{3} and g′(32)=−2g'\left(\dfrac{\sqrt{3}}{2}\right) = -2, then the derivative of f(sin⁡x)f(\sin x) with respect to g(cos⁡x)g(\cos x) at x=π6x = \dfrac{\pi}{6} is:

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