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dy/dx of a curve given in parametric form

This type of question, asked 7 times: 2 May 2023 S2, 13 May 2024 S2, 22 Apr 2025 S1, 23 Apr 2025 S1, 13 May 2026 S1, 14 May 2026 S1, 14 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    120
    If x=sec⁡θ−cos⁡θ,  y=sec⁡10θ−cos⁡10θx = \sec\theta - \cos\theta,\; y = \sec^{10}\theta - \cos^{10}\theta and (x2+4)(dydx)2=k(y2+4)\left(x^2+4\right)\left(\frac{dy}{dx}\right)^2 = k(y^2+4), then the value of k is

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  2. Question 2

    13 May 2024 S2

    122
    If x=log⁡e ⁣cos⁡y2−sin⁡y2cos⁡y2+sin⁡y2, tan⁡y2=1−t1+tx=\log_e\!\frac{\cos\frac{y}{2}-\sin\frac{y}{2}}{\cos\frac{y}{2}+\sin\frac{y}{2}},\ \tan\frac{y}{2}=\frac{1-t}{1+t}. Then y′ ⁣ ⁣∣t=12y'\!\!\left|_{t=\frac{1}{2}}\right. has the value

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  3. Question 3

    22 Apr 2025 S1

    147
    If x=acos3θy=asin3θx=acos^{3}\theta y=asin^{3}\theta Then 1+(dy dx)2=\sqrt{1 +\left( \frac{dy}{\text{ }dx} \right)^{2}}=

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  4. Question 4

    23 Apr 2025 S1

    136
    If x=asin2t (1+cos⁡2t),y=bcos2t (1−cos⁡2t)x=asin2t\ (1 + \cos2t),y=bcos2t\ (1 - \cos2t) then dy dx\frac{dy}{\text{ }dx} is equal to

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  5. Question 5

    13 May 2026 S1

    74
    If x=2tan⁡−1tx = \sqrt{2^{\tan^{-1}t}} and y=2cot⁡−1t3y = \sqrt[3]{2^{\cot^{-1}t}}, then dydx=…\dfrac{dy}{dx} = \ldots

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  6. Question 6

    14 May 2026 S1

    73
    If x=em+e−m2x = \dfrac{e^m + e^{-m}}{2} and y=em−e−m2y = \dfrac{e^m - e^{-m}}{2} then dydx=\dfrac{dy}{dx} =

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  7. Question 7

    14 May 2026 S2

    73
    If x=1+log⁡tt2x = \dfrac{1 + \log t}{t^2} and y=3+2log⁡tty = \dfrac{3 + 2\log t}{t}, then the value of dydx\dfrac{dy}{dx} is

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