Misc 12 - Find dy/dx, if y =12 (1 - cos t), x = 10 (t-sin t) - Miscellaneous

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Misc 12 Find 𝑑𝑦﷮𝑑𝑥﷯, if 𝑦=12 1 – cos﷮𝑡﷯﷯, 𝑥=10 𝑡 – sin﷮𝑡﷯﷯,− 𝜋﷮2﷯ <𝑥< 𝜋﷮2﷯ 𝑦=12 1 – cos﷮𝑡﷯﷯ & 𝑥=10 𝑡 – sin﷮𝑡﷯﷯ We need to find 𝑑𝑦﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦﷮𝑑𝑥﷯ × 𝑑𝑡﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦﷮𝑑𝑡﷯ × 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦/𝑑𝑡﷮𝑑𝑥/𝑑𝑡﷯ Calculating 𝒅𝒚﷮𝒅𝒕﷯ 𝑦=12 1 – cos﷮𝑡﷯﷯ 𝑦=12 −12 cos﷮𝑡﷯ Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦﷮𝑑𝑡﷯ = 𝑑 12 −12 cos﷮𝑡﷯﷯﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑡﷯ = 𝑑 12﷯﷮𝑑𝑡﷯ − 12 𝑑 cos﷮𝑡﷯﷯﷮𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑡﷯ = 0 − 12 − sin﷮𝑡﷯﷯ 𝑑𝑦﷮𝑑𝑡﷯ = 12 sin﷮𝑡﷯ Therefore 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑𝑦/𝑑𝑡﷮𝑑𝑥/𝑑𝑡﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 12 sin﷮𝑡﷯﷮10 1 − cos﷮𝑡﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 6 sin﷮𝑡﷯﷮5 1 − cos﷮𝑡﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 6 . 2 sin ﷮ 𝑡﷮2﷯﷯ cos﷮ 𝑡﷮2﷯﷯﷮5 2 sin﷮2﷯﷮ 𝑡﷮2﷯﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 6 cos﷮ 𝑡﷮2﷯﷯﷮5 sin ﷮ 𝑡﷮2﷯﷯ ﷯ 𝒅𝒚﷮𝒅𝒙﷯ = 𝟔﷮𝟓﷯ 𝒄𝒐𝒕 𝒕﷮𝟐﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 6 2 sin﷮ 𝑡﷮2﷯﷯ − cos﷮ 𝑡﷮2﷯﷯﷯﷮5 1 − 1 − 2 sin﷮2﷯﷮ 𝑡﷮2﷯﷯﷯﷯﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.