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

Transcript

Misc 8 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): (ax + b)/(px2 + qx + r) Let f(x) = (๐‘Ž๐‘ฅ + ๐‘)/(๐‘๐‘ฅ2 + ๐‘ž๐‘ฅ + ๐‘Ÿ) Let u = ax + b & v = px2 +qx+ r 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 = ax + b uโ€™ = a ร— 1 + 0 uโ€™ = a v = px2 + qx + r vโ€™= p ร— 2x + q ร— 1 + 0 vโ€™ = 2px + q 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 = (๐‘Ž (๐‘๐‘ฅ2 + ๐‘ž๐‘ฅ + ๐‘Ÿ ) โˆ’ (2๐‘๐‘ฅ + ๐‘ž) (๐‘Ž๐‘ฅ + ๐‘) )/(๐‘๐‘ฅ2+ ๐‘ž๐‘ฅ + ๐‘Ÿ)2 = (๐‘Ž๐‘๐‘ฅ2 + ๐‘Ž๐‘ž๐‘ฅ + ๐‘Ž๐‘Ÿ โˆ’ 2๐‘๐‘ฅ (๐‘Ž๐‘ฅ + ๐‘) โˆ’ ๐‘ž (๐‘Ž๐‘ฅ + ๐‘) )/(๐‘๐‘ฅ2+ ๐‘ž๐‘ฅ + ๐‘Ÿ)2 = (๐‘Ž๐‘๐‘ฅ2 โˆ’ 2๐‘Ž๐‘๐‘ฅ2 + ๐‘Ž๐‘ž๐‘ฅ โˆ’ ๐‘Ž๐‘ž๐‘ฅ โˆ’ 2๐‘๐‘๐‘ฅ โˆ’ ๐‘ž๐‘ + ๐‘Ž๐‘Ÿ )/(๐‘๐‘ฅ2+ ๐‘ž๐‘ฅ + ๐‘Ÿ)2 = (โˆ’ ๐‘Ž๐‘๐‘ฅ2 โˆ’ 2๐‘Ž๐‘๐‘ฅ โˆ’ ๐‘ž๐‘ + ๐‘Ž๐‘Ÿ )/(๐‘๐‘ฅ2+ ๐‘ž๐‘ฅ + ๐‘Ÿ)2 = (โˆ’ ๐‘Ž๐‘๐‘ฅ2 โˆ’ 2๐‘Ž๐‘๐‘ฅ + ๐‘Ž๐‘Ÿ โˆ’ ๐‘๐‘ž)/(๐‘๐‘ฅ2+ ๐‘ž๐‘ฅ + ๐‘Ÿ)2 So, fโ€™(x) = (โˆ’ ๐’‚๐’‘๐’™๐Ÿ โˆ’ ๐Ÿ๐’‚๐’ƒ๐’™ + ๐’‚๐’“ โˆ’ ๐’ƒ๐’’)/(๐’‘๐’™๐Ÿ+ ๐’’๐’™ + ๐’“)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.