Ex 5.6, 3 - Find dy/dx, x = sin t, y = cos 2t - Class 12 - Ex 5.6

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.6, 3 If x and y are connected parametrically by the equations without eliminating the parameter, Find 𝑑𝑦﷮𝑑𝑥﷯, 𝑥= sin﷮𝑡﷯, 𝑦=cos⁡2𝑡 𝑥= sin﷮𝑡﷯, 𝑦=cos⁡2𝑡 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦﷮𝑑𝑥﷯ × 𝑑𝑡﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦﷮𝑑𝑡﷯ × 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦﷮𝑑𝑡﷯﷮ 𝑑𝑥﷮𝑑𝑡﷯﷯ Calculating 𝒅𝒚﷮𝒅𝒕﷯ 𝑑𝑦﷮𝑑𝑡﷯ = 𝑑 cos⁡2𝑡﷯﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑡﷯ = −sin⁡2𝑡 . 𝑑 2𝑡﷯﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑡﷯ = −sin⁡2𝑡 . 2 𝑑𝑦﷮𝑑𝑡﷯ = −2 sin⁡2𝑡

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