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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise

Transcript

Misc 9 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (px2 + qx + r)/(ax + b) Let f(x) = (๐‘๐‘ฅ2 + ๐‘ž๐‘ฅ + ๐‘Ÿ)/(๐‘Ž๐‘ฅ + ๐‘) Let u = px2 + qx + r & v = ax + b โˆด f(x) = ๐‘ข/๐‘ฃ So, fโ€™(x) = (๐‘ข/๐‘ฃ)^โ€ฒ fโ€™(x) = (๐‘ข^โ€ฒ ๐‘ฃ โˆ’ ๐‘ฃ^โ€ฒ ๐‘ข)/๐‘ฃ^2 Finding uโ€™ & vโ€™ u = px2 + qx + r uโ€™ = p ร— 2x + q ร— 1 + 0 uโ€™ = 2px + q v = ax + 3 vโ€™= a ร— 1 + 0 vโ€™ = a fโ€™(x) = (๐‘ข/๐‘ฃ)^โ€ฒ = (๐‘ข^โ€ฒ ๐‘ฃ โˆ’ใ€– ๐‘ฃใ€—^โ€ฒ ๐‘ข)/๐‘ฃ^2 = ((2๐‘๐‘ฅ + ๐‘ž) (๐‘Ž๐‘ฅ + ๐‘) โˆ’ a (px2 + ๐‘ž๐‘ฅ + ๐‘Ÿ) )/(ax + b)2 = (2๐‘Ž๐‘๐‘ฅ2 + 2๐‘๐‘๐‘ฅ + ๐‘ž๐‘Ž๐‘ฅ + ๐‘๐‘ž โˆ’ ๐‘Ž๐‘๐‘ฅ2 โˆ’ ๐‘ž๐‘Ž๐‘ฅ โˆ’ ๐‘Ž๐‘Ÿ)/(ax + b)2 = (๐‘Ž๐‘๐‘ฅ2 + 2๐‘๐‘๐‘ฅ + ๐‘๐‘ž โˆ’ ๐‘Ž๐‘Ÿ )/(ax + b)2 โˆด fโ€™(x) = (๐’‚๐’‘๐’™๐Ÿ + ๐Ÿ๐’ƒ๐’‘๐’™ + ๐’ƒ๐’’ โˆ’ ๐’‚๐’“)/(๐’‚๐’™ + ๐’ƒ)๐Ÿ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.