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Value of dy/dx at a given point of an implicitly defined curve

This type of question, asked 9 times: 10 May 2023 S1, 10 May 2023 S2, 15 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1, 13 May 2024 S2, 18 Apr 2026 S1, 19 Apr 2026 S2. All 10 questions below, oldest first.

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  1. Question 1

    10 May 2023 S1

    136
    If y is a function of x and log⁡(x+y)=2xy\log(x+y)=2xy, then the value of y′(0)y'(0) is

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  2. Question 2

    10 May 2023 S2

    104
    If y is a function of x and log⁡(x+y)=2xy\log(x+y) = 2xy, then the value of y′(0)y'(0) is

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  3. Question 3

    10 May 2023 S2

    116
    If x2y2=sin⁡−1x+cos⁡−1xx^2 y^2 = \sin^{-1}x + \cos^{-1}x, then dydx\frac{dy}{dx} at x=1x=1 and y=2y=2 is

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  4. Question 4

    15 May 2023 S1

    115
    If (a+2bcos⁡x)(a−2bcos⁡y)=a2−b2(a+2b\cos x)(a-2b\cos y) = a^{2}-b^{2}, where a>b>0a>b>0, then dxdy\frac{dx}{dy} at (π4,π4)\left(\frac{\pi}{4},\frac{\pi}{4}\right) is

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  5. Question 5

    9 May 2024 S2

    126
    If yy is a function of xx and log⁡(x+y)=2xy\log(x+y) = 2xy, then the value of y′(0)y'(0) is

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  6. Question 6

    10 May 2024 S2

    129
    If yy is a function of xx and log⁡(x+y)=2xy\log(x+y)=2xy, then dydx\dfrac{dy}{dx} at x=0x=0 is

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  7. Question 7

    12 May 2024 S1

    133
    If log⁡(x+y)=2xy\log(x+y)=2xy, then dydx\frac{dy}{dx} at x=0x=0 is

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  8. Question 8

    13 May 2024 S2

    127
    If slope of the tangent to the curve xy+ax+by=0xy+ax+by=0 at the point (1,1)(1,1) on it is 2, then the value of 3a+b3a+b is

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  9. Question 9

    18 Apr 2026 S1

    74
    If x exy=y+sin⁡2xx\,e^{xy} = y + \sin^2 x, then the value of dydx\dfrac{dy}{dx} at x=0x = 0 is equal to

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  10. Question 10

    19 Apr 2026 S2

    74
    If 3y2−2xy−x=03y^2 - 2xy - x = 0, then the value of dydx\dfrac{dy}{dx} at y=2y = 2 is...

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