Ex 5.3, 5 - Find dy/dx in, x2 + xy + y2 = 100 - Class 12 - Finding derivative of Implicit functions

Slide8.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.3, 5 Find ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ in, ๐‘ฅ2 + ๐‘ฅ๐‘ฆ + ๐‘ฆ2 = 100 ๐‘ฅ2 + ๐‘ฅ๐‘ฆ + ๐‘ฆ2 = 100 Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ . ๐‘‘(๐‘ฅ2 + ๐‘ฅ๐‘ฆ + ๐‘ฆ2)/๐‘‘๐‘ฅ = (๐‘‘ (100))/๐‘‘๐‘ฅ ๐‘‘(๐‘ฅ2)/๐‘‘๐‘ฅ + ๐‘‘(๐‘ฅ๐‘ฆ)/๐‘‘๐‘ฅ + (๐‘‘(๐‘ฆ2))/๐‘‘๐‘ฅ = (๐‘‘ (100))/๐‘‘๐‘ฅ 2๐‘ฅ^(2โˆ’1) + (๐‘‘(๐‘ฅ๐‘ฆ))/๐‘‘๐‘ฅ + (๐‘‘(๐‘ฆ2))/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฆ = 0 2๐‘ฅ + (๐‘‘(๐‘ฅ๐‘ฆ))/๐‘‘๐‘ฅ + (๐‘‘(๐‘ฆ2))/๐‘‘๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 2๐‘ฅ + (๐‘‘(๐‘ฅ๐‘ฆ))/๐‘‘๐‘ฅ + 2๐‘ฆ^(2โˆ’1) . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 2๐‘ฅ + (๐‘‘(๐‘ฅ๐‘ฆ))/๐‘‘๐‘ฅ + 2๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 Using product rule in ๐‘ฅ๐‘ฆ = ๐‘ฅ^โ€ฒ ๐‘ฆ+๐‘ฆ^โ€ฒ ๐‘ฅ 2๐‘ฅ + ((๐‘‘(๐‘ฅ))/๐‘‘๐‘ฅ .๐‘ฆ+๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ.๐‘ฅ) + 2๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 2๐‘ฅ + (1 .๐‘ฆ+๐‘ฅ.๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ) + 2๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 2๐‘ฅ + ๐‘ฆ + ๐‘ฅ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ + 2๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 0 (2๐‘ฅ + ๐‘ฆ) + ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ . (๐‘ฅ + 2๐‘ฆ) = 0 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ . (๐‘ฅ + 2๐‘ฆ) = โˆ’ (2๐‘ฅ + ๐‘ฆ) ๐’…๐’š/๐’…๐’™ = (โˆ’( ๐Ÿ๐’™ + ๐’š ))/( ( ๐’™ + ๐Ÿ๐’š ))

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.