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Second derivative of an implicitly defined curve

This type of question, asked 3 times: 25 Apr 2025 S1, 15 Apr 2026 S2, 19 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    25 Apr 2025 S1

    109
    If x2a2+y2 b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1, then d2y dx2\frac{d^{2}y}{\text{ }dx^{2}} is

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  2. Question 2

    15 Apr 2026 S2

    73
    If ey+xy=ee^y + xy = e, then the ordered pair (dydx,d2ydx2)\left(\dfrac{dy}{dx}, \dfrac{d^2y}{dx^2}\right) at x=0x = 0 is equal to

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  3. Question 3

    19 Apr 2026 S2

    71
    If xm+ym=k,(m≠1)x^m + y^m = k, (m \neq 1) and y′′=axbycy'' = \dfrac{ax^b}{y^c} such that a+b+c=0a + b + c = 0, then the value of k is...

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