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Ex 5.3, 5 - Find dy/dx in, x2 + xy + y2 = 100 - Class 12

Ex 5.3, 5 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Transcript

Ex 5.3, 5 Find 𝑑𝑦/𝑑𝑥 in, 𝑥2 + 𝑥𝑦 + 𝑦2 = 100 𝑥2 + 𝑥𝑦 + 𝑦2 = 100 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . 𝑑(𝑥2 + 𝑥𝑦 + 𝑦2)/𝑑𝑥 = (𝑑 (100))/𝑑𝑥 𝑑(𝑥2)/𝑑𝑥 + 𝑑(𝑥𝑦)/𝑑𝑥 + (𝑑(𝑦2))/𝑑𝑥 = (𝑑 (100))/𝑑𝑥 2𝑥^(2−1) + (𝑑(𝑥𝑦))/𝑑𝑥 + (𝑑(𝑦2))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 = 0 2𝑥 + (𝑑(𝑥𝑦))/𝑑𝑥 + (𝑑(𝑦2))/𝑑𝑦 × 𝑑𝑦/𝑑𝑥 = 0 As (𝑥^𝑛 )^′=𝑛𝑥^(𝑛−1) & derivative of a constant is zero 2𝑥 + (𝑑(𝑥𝑦))/𝑑𝑥 + 2𝑦^(2−1) . 𝑑𝑦/𝑑𝑥 = 0 2𝑥 + (𝑑(𝑥𝑦))/𝑑𝑥 + 2𝑦 . 𝑑𝑦/𝑑𝑥 = 0 Using product rule in 𝑥𝑦 = 𝑥^′ 𝑦+𝑦^′ 𝑥 2𝑥 + ((𝑑(𝑥))/𝑑𝑥 .𝑦+𝑑(𝑦)/𝑑𝑥.𝑥) + 2𝑦 . 𝑑𝑦/𝑑𝑥 = 0 2𝑥 + (1 .𝑦+𝑥.𝑑(𝑦)/𝑑𝑥) + 2𝑦 . 𝑑𝑦/𝑑𝑥 = 0 2𝑥 + 𝑦 + 𝑥 . 𝑑𝑦/𝑑𝑥 + 2𝑦 . 𝑑𝑦/𝑑𝑥 = 0 (2𝑥 + 𝑦) + 𝑑𝑦/𝑑𝑥 . (𝑥 + 2𝑦) = 0 𝑑𝑦/𝑑𝑥 . (𝑥 + 2𝑦) = − (2𝑥 + 𝑦) 𝒅𝒚/𝒅𝒙 = (−( 𝟐𝒙 + 𝒚 ))/( ( 𝒙 + 𝟐𝒚 ))

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.