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Implicit relation that reduces to y/x or x + y constant, so dy/dx is immediate

This type of question, asked 5 times: 9 May 2023 S2, 11 May 2023 S1, 9 May 2024 S1, 20 Apr 2026 S2, 14 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    9 May 2023 S2

    118
    If log⁡(x+y)=sin⁡(x+y)\log(x+y) = \sin(x+y), then dydx\frac{dy}{dx} is

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  2. Question 2

    11 May 2023 S1

    121
    If x2+y2=t+1tx^2 + y^2 = t + \frac{1}{t}, x4+y4=t2+1t2x^4 + y^4 = t^2 + \frac{1}{t^2}, then dydx=\frac{dy}{dx} =

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  3. Question 3

    9 May 2024 S1

    102
    If x2+y2=t+1tx^2+y^2=t+\frac{1}{t} and x4+y4=t2+1t2x^4+y^4=t^2+\frac{1}{t^2}, then dydx\frac{dy}{dx} is equal to

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  4. Question 4

    20 Apr 2026 S2

    72
    If xy+yx=6\sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} = 6, then dydx=\dfrac{dy}{dx} =

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  5. Question 5

    14 May 2026 S2

    75
    If 3x2+4xy+5y2=03x^2 + 4xy + 5y^2 = 0, then dydx=…\dfrac{dy}{dx} = \ldots

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