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Last updated at Nov. 30, 2019 by Teachoo

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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) = (๐๐ฅ2 + ๐๐ฅ + ๐)/(๐๐ฅ + ๐) Let u = px2 + qx + r & v = ax + b โด f(x) = ๐ข/๐ฃ So, fโ(x) = (๐ข/๐ฃ)^โฒ fโ(x) = (๐ข^โฒ ๐ฃ โ ๐ฃ^โฒ ๐ข)/๐ฃ^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) = (๐ข/๐ฃ)^โฒ = (๐ข^โฒ ๐ฃ โใ ๐ฃใ^โฒ ๐ข)/๐ฃ^2 = ((2๐๐ฅ + ๐) (๐๐ฅ + ๐) โ a (px2 + ๐๐ฅ + ๐) )/(ax + b)2 = (2๐๐๐ฅ2 + 2๐๐๐ฅ + ๐๐๐ฅ + ๐๐ โ ๐๐๐ฅ2 โ ๐๐๐ฅ โ ๐๐)/(ax + b)2 = (๐๐๐ฅ2 + 2๐๐๐ฅ + ๐๐ โ ๐๐ )/(ax + b)2 โด fโ(x) = (๐๐๐๐ + ๐๐๐๐ + ๐๐ โ ๐๐)/(๐๐ + ๐)๐

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About the Author

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.