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sqrt(y + x) + sqrt(y - x) = c: write dy/dx in the given form and find the missing function

The same question, asked 2 times: 13 Apr 2026 S2, 20 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    13 Apr 2026 S2

    73
    If y+x+y−x=c\sqrt{y + x} + \sqrt{y - x} = c such that dydx=f(x)−[f(x)]2−1\dfrac{dy}{dx} = f(x) - \sqrt{[f(x)]^2 - 1}, then f(x)=f(x) = ____

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  2. Question 2

    20 Apr 2026 S1

    71
    If y+x+y−x=c\sqrt{y + x} + \sqrt{y - x} = c and dydx=K−y2x2−1\dfrac{dy}{dx} = K - \sqrt{\dfrac{y^2}{x^2} - 1}, then the value of KK is

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