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dy/dx of y = f(u(x)) when f or f' is given

This type of question, asked 3 times: 14 May 2024 S2, 11 Apr 2026 S1, 18 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    14 May 2024 S2

    109
    If f′(x)=sin⁡(log⁡x)f'(x) = \sin(\log x) and y=f ⁣(2x+33−2x)y = f\!\left(\frac{2x+3}{3-2x}\right), then dydx\frac{dy}{dx} at x=1x=1 is

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  2. Question 2

    11 Apr 2026 S1

    69
    If y=f(3+2x3−2x)y = f\left(\dfrac{3 + 2x}{3 - 2x}\right), where f(x)=tan⁡(log⁡x)f(x) = \tan(\log x) and dydx=(AB+Cx2)⋅sec⁡2(log⁡(3+2x3−2x))\dfrac{dy}{dx} = \left(\dfrac{A}{B + Cx^2}\right)\cdot\sec^2\left(\log\left(\dfrac{3 + 2x}{3 - 2x}\right)\right), then the respective values of A, B and C are ......

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  3. Question 3

    18 Apr 2026 S2

    73
    If f′(x)=sin⁡2xf'(x) = \sin^2 x and y=f(2x−1x2+1)y = f\left(\dfrac{2x - 1}{x^2 + 1}\right), then dydx\dfrac{dy}{dx} at x=1x = 1 is

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