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

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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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Ex 5.3, 5 Find š‘‘š‘¦/š‘‘š‘„ in, š‘„2 + š‘„š‘¦ + š‘¦2 = 100 š‘„2 + š‘„š‘¦ + š‘¦2 = 100 Differentiating both sides š‘¤.š‘Ÿ.š‘”.š‘„ . š‘‘(š‘„2 + š‘„š‘¦ + š‘¦2)/š‘‘š‘„ = (š‘‘ (100))/š‘‘š‘„ š‘‘(š‘„2)/š‘‘š‘„ + š‘‘(š‘„š‘¦)/š‘‘š‘„ + (š‘‘(š‘¦2))/š‘‘š‘„ = (š‘‘ (100))/š‘‘š‘„ 2š‘„^(2āˆ’1) + (š‘‘(š‘„š‘¦))/š‘‘š‘„ + (š‘‘(š‘¦2))/š‘‘š‘„ Ɨ š‘‘š‘¦/š‘‘š‘¦ = 0 2š‘„ + (š‘‘(š‘„š‘¦))/š‘‘š‘„ + (š‘‘(š‘¦2))/š‘‘š‘¦ Ɨ š‘‘š‘¦/š‘‘š‘„ = 0 As (š‘„^š‘› )^ā€²=š‘›š‘„^(š‘›āˆ’1) & derivative of a constant is zero 2š‘„ + (š‘‘(š‘„š‘¦))/š‘‘š‘„ + 2š‘¦^(2āˆ’1) . š‘‘š‘¦/š‘‘š‘„ = 0 2š‘„ + (š‘‘(š‘„š‘¦))/š‘‘š‘„ + 2š‘¦ . š‘‘š‘¦/š‘‘š‘„ = 0 Using product rule in š‘„š‘¦ = š‘„^ā€² š‘¦+š‘¦^ā€² š‘„ 2š‘„ + ((š‘‘(š‘„))/š‘‘š‘„ .š‘¦+š‘‘(š‘¦)/š‘‘š‘„.š‘„) + 2š‘¦ . š‘‘š‘¦/š‘‘š‘„ = 0 2š‘„ + (1 .š‘¦+š‘„.š‘‘(š‘¦)/š‘‘š‘„) + 2š‘¦ . š‘‘š‘¦/š‘‘š‘„ = 0 2š‘„ + š‘¦ + š‘„ . š‘‘š‘¦/š‘‘š‘„ + 2š‘¦ . š‘‘š‘¦/š‘‘š‘„ = 0 (2š‘„ + š‘¦) + š‘‘š‘¦/š‘‘š‘„ . (š‘„ + 2š‘¦) = 0 š‘‘š‘¦/š‘‘š‘„ . (š‘„ + 2š‘¦) = āˆ’ (2š‘„ + š‘¦) š’…š’š/š’…š’™ = (āˆ’( šŸš’™ + š’š ))/( ( š’™ + šŸš’š ))

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