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Ex 5.3, 6 - Find dy/dx in x3 + x2y + xy2 + y3 = 81 - CBSE

Ex 5.3, 6 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Ex 5.3, 6 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

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Ex 5.3, 6 Find š‘‘š‘¦/š‘‘š‘„ in, š‘„3 + š‘„2š‘¦ + š‘„š‘¦2 + š‘¦3 = 81 š‘„3 + š‘„2š‘¦ + š‘„š‘¦2 + š‘¦3 = 81 Differentiating both sides š‘¤.š‘Ÿ.š‘”.š‘„ . š‘‘(š‘„3 + š‘„2š‘¦ + š‘„š‘¦2 + š‘¦3)/š‘‘š‘„ = (š‘‘ (81))/š‘‘š‘„ š‘‘(š‘„3)/š‘‘š‘„ + š‘‘(š‘„2š‘¦)/š‘‘š‘„ + (š‘‘(š‘„š‘¦2))/š‘‘š‘„ + š‘‘(š‘¦3)/š‘‘š‘„ =0 3š‘„^(3āˆ’1) + (š‘‘(š‘„2š‘¦))/š‘‘š‘„ + (š‘‘(š‘„š‘¦2))/š‘‘š‘„ + š‘‘(š‘¦3)/š‘‘š‘„ Ɨ š‘‘š‘¦/š‘‘š‘¦ = 0 3š‘„^2 + (š‘‘(š‘„2š‘¦))/š‘‘š‘„ + (š‘‘(š‘„š‘¦2))/š‘‘š‘„ + š‘‘(š‘¦3)/š‘‘š‘„ Ɨ š‘‘š‘¦/š‘‘š‘„ = 0 3š‘„^2+ (š‘‘(š‘„2š‘¦))/š‘‘š‘„ + (š‘‘(š‘„š‘¦2))/š‘‘š‘„ +3š‘¦^(3āˆ’1) . š‘‘š‘¦/š‘‘š‘„ = 0 3š‘„2 + (š‘‘(š‘„2š‘¦))/š‘‘š‘„ + (š‘‘(š‘„š‘¦2))/š‘‘š‘„ +3š‘¦^2 š‘‘š‘¦/š‘‘š‘„ = 0 Using product rule in š‘„2š‘¦ & š‘„š‘¦2 (uv)ā€™ = uā€™v + vā€™u 3š‘„2 + ((š‘‘(š‘„2))/š‘‘š‘„.š‘¦+š‘„2 .(š‘‘(š‘¦))/š‘‘š‘„)+((š‘‘(š‘„))/š‘‘š‘„.š‘¦2+ .(š‘‘(š‘¦2))/š‘‘š‘„ š‘„ )+ 3y2 š‘‘š‘¦/( š‘‘š‘„) = 0 3š‘„2 + (2š‘„.š‘¦+š‘„2 (š‘‘(š‘¦))/š‘‘š‘„) + (1.š‘¦2+š‘„ .(š‘‘(š‘¦2))/š‘‘š‘„ )+ 3y2 š‘‘š‘¦/( š‘‘š‘„) = 0 3š‘„2 + (2š‘„.š‘¦+š‘„2 (š‘‘(š‘¦))/š‘‘š‘„) + (š‘¦2+š‘„ .(š‘‘(š‘¦2))/š‘‘š‘„ Ɨ š‘‘š‘¦/š‘‘š‘¦)+ 3y2 š‘‘š‘¦/( š‘‘š‘„) = 0 3š‘„2 + 2š‘„š‘¦+š‘„2 š‘‘š‘¦/š‘‘š‘„+š‘¦2+š‘„.(š‘‘(š‘¦2))/š‘‘š‘¦ Ɨš‘‘š‘¦/š‘‘š‘„+3š‘¦2 š‘‘š‘¦/( š‘‘š‘„) = 0 3š‘„2 + 2š‘„š‘¦+š‘„2 š‘‘š‘¦/š‘‘š‘„+š‘¦2 + š‘„. 2š‘¦^(2āˆ’1) (š‘‘š‘¦/š‘‘š‘„)+3š‘¦2 š‘‘š‘¦/š‘‘š‘„=0 3š‘„2 + 2š‘„š‘¦+š‘¦2 + x2 š‘‘š‘¦/š‘‘š‘„+š‘„.2š‘¦ š‘‘š‘¦/š‘‘š‘„+3š‘¦2 š‘‘š‘¦/š‘‘š‘„=0 "(3" š‘„"2 "+" " 2š‘„š‘¦+š‘¦2")" + š‘‘š‘¦/š‘‘š‘„ (š‘„2+2š‘„š‘¦+3š‘¦2)=0 š‘‘š‘¦/š‘‘š‘„ (š‘„2+2š‘„š‘¦+3š‘¦2)=āˆ’ "(3" š‘„"2 "+" " 2š‘„š‘¦+š‘¦2")" š’…š’š/š’…š’™= (āˆ’ "(" šŸ‘š’™"2 " +" " šŸš’™š’š + š’ššŸ")" )/((š’™šŸ + šŸš’™š’š + šŸ‘š’ššŸ) )

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.