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Ex 5.3, 8 - Find dy/dx in, sin2 x + cos2 y = 1 - Class 12 - Finding derivative of Implicit functions

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.3, 8 Find 𝑑𝑦﷮𝑑𝑥﷯ in, sin2 𝑥 + cos2 𝑦 = 1 sin2 𝑥 + cos2 𝑦 = 1 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . 𝑑 sin2 𝑥 + cos2 𝑦﷯﷮𝑑𝑥﷯ = 𝑑 1﷯﷮𝑑𝑥﷯ 𝑑 (sin2 𝑥)﷮𝑑𝑥﷯ + 𝑑 ( cos﷮2﷯ 𝑦)﷮𝑑𝑥﷯ = 0 Calculating Derivative of sin2 𝑥 & cos﷮2﷯ 𝑦 sepretaly Finding Derivative of 𝒔𝒊𝒏𝟐 𝒙 𝑑 (sin2 𝑥)﷮𝑑𝑥﷯ =2 𝑠𝑖𝑛﷮2−1﷯ 𝑥 . 𝑑( sin﷮2﷯﷮𝑥﷯)﷮𝑑𝑥﷯ =2 sin﷮𝑥﷯ . 𝑑( sin﷮𝑥﷯)﷮𝑑𝑥﷯ =2 sin﷮𝑥 cos﷮𝑥﷯﷯ Finding Derivative of 𝒄𝒐𝒔﷮𝟐﷯ 𝒚 𝑑 (cos2 𝑦)﷮𝑑𝑥﷯ =2 cos﷮𝑦﷯﷮2−1﷯ . 𝑑﷮𝑑𝑥﷯ ( cos﷮𝑦﷯) =2 cos﷮𝑦﷯ . (−sin⁡𝑦) . 𝑑(𝑦)﷮𝑑𝑥﷯ =− 2 cos﷮𝑦﷯ sin⁡𝑦 . 𝑑𝑦﷮𝑑𝑥﷯ Now, 𝑑 (sin2 𝑥)﷮𝑑𝑥﷯+ 𝑑 (cos2 𝑦)﷮𝑑𝑥﷯ = 0 2 sin﷮𝑥﷯ . cos﷮𝑥﷯ + − 2 cos⁡𝑦 sin⁡𝑦 . 𝑑𝑦﷮𝑑𝑥﷯﷯= 0 2 sin﷮𝑥﷯ . cos﷮𝑥﷯ − 2 sin﷮𝑦﷯﷮ .﷯ cos﷮𝑦﷯ . 𝑑𝑦﷮𝑑𝑥﷯ = 0 − 2 sin﷮𝑦﷯﷮ .﷯ cos﷮𝑦﷯ . 𝑑𝑦﷮𝑑𝑥﷯ = − 2 sin﷮𝑥﷯ cos﷮𝑥﷯ − sin﷮2𝑦﷯﷮ .﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − sin﷮2𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − sin﷮2𝑥﷯﷮− sin﷮2𝑦﷯﷯ 𝒅𝒚﷮𝒅𝒙﷯ = 𝒔𝒊𝒏﷮𝟐𝒙﷯﷮ 𝒔𝒊𝒏﷮𝟐𝒚﷯﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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