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dy/dx for x^k + y^k = a^k

This type of question, asked 2 times: 9 May 2024 S2, 19 Apr 2025 S2. All 2 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    137
    If xk+yk=ak    (a,k>0)x^k + y^k = a^k\;\;(a,k > 0) and dydx+(yx)1/3=0\dfrac{dy}{dx} + \left(\dfrac{y}{x}\right)^{1/3} = 0, then kk has the value

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  2. Question 2

    19 Apr 2025 S2

    115
    If x25+y25=a25x^{\frac{2}{5}}+y^{\frac{2}{5}}=a^{\frac{2}{5}} then dy dx=\frac{dy}{\text{ }dx}=

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