# Ex 5.5, 13 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.5, 13 Find 𝑑𝑦𝑑𝑥 of the functions in, 𝑦𝑥 = 𝑥𝑦 Given , 𝑦𝑥 = 𝑥𝑦 Taking log both sides log 𝑦𝑥 = log 𝑥𝑦 𝑥 . log 𝑦=𝑦. log𝑥 Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑(𝑥 . log 𝑦)𝑑𝑥 = 𝑑 𝑦. log𝑥𝑑𝑥 𝑑 𝑥𝑑𝑥 . log 𝑦+ 𝑑 log𝑦𝑑𝑥 . 𝑥 = 𝑑 𝑦𝑑𝑥 . log 𝑥 + 𝑑 log𝑥𝑑𝑥 . 𝑦 log 𝑦+𝑥 . 𝑑 log𝑦𝑑𝑥 . 𝑥 = 𝑑𝑦𝑑𝑥 log 𝑥 + 1𝑥 . 𝑦 log 𝑦+𝑥 . 𝑑 log𝑦𝑑𝑥 . 𝑑𝑦𝑑𝑦 = 𝑑𝑦𝑑𝑥 . log 𝑥 + 𝑦𝑥 log 𝑦+𝑥 . 𝑑 log𝑦𝑑𝑦 . 𝑑𝑦𝑑𝑥 = 𝑑𝑦𝑑𝑥 . log 𝑥 + 𝑦𝑥 log 𝑦+𝑥 . 1𝑦 . 𝑑𝑦𝑑𝑥 = 𝑑𝑦𝑑𝑥 . log 𝑥 + 𝑦𝑥 log 𝑦+ 𝑥𝑦 . 𝑑𝑦𝑑𝑥 = 𝑑𝑦𝑑𝑥 . log 𝑥 + 𝑦𝑥 𝑥𝑦 . 𝑑𝑦𝑑𝑥 − 𝑑𝑦𝑑𝑥 . log 𝑥 = 𝑦𝑥 − log 𝑦 𝑑𝑦𝑑𝑥 𝑥𝑦 − log 𝑥 = 𝑦𝑥 − log 𝑦 𝑑𝑦𝑑𝑥 𝑥 − 𝑦 log𝑥𝑦 = 𝑦 − 𝑥 log𝑦𝑥 𝑑𝑦𝑑𝑥 = 𝑦 − 𝑥 log𝑦𝑥 . 𝑦𝑥 − 𝑦 log𝑥 𝒅𝒚𝒅𝒙 = 𝒚 𝒚 − 𝒙 𝒍𝒐𝒈𝒚𝒙 𝒙 − 𝒚 𝒍𝒐𝒈𝒙

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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.