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Misc 9 - Find derivative: px2 + qx + r / ax + b - Chapter 13

Misc 9 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Misc 9 - Chapter 13 Class 11 Limits and Derivatives - Part 3

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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) = (š‘š‘„2 + š‘žš‘„ + š‘Ÿ)/(š‘Žš‘„ + š‘) Let u = px2 + qx + r & v = ax + b āˆ“ f(x) = š‘¢/š‘£ So, fā€™(x) = (š‘¢/š‘£)^ā€² fā€™(x) = (š‘¢^ā€² š‘£ āˆ’ š‘£^ā€² š‘¢)/š‘£^2 Finding uā€™ & vā€™ u = px2 + qx + r uā€™ = p Ɨ 2x + q Ɨ 1 + 0 uā€™ = 2px + q v = ax + 3 vā€™= a Ɨ 1 + 0 vā€™ = a fā€™(x) = (š‘¢/š‘£)^ā€² = (š‘¢^ā€² š‘£ āˆ’怖 š‘£ć€—^ā€² š‘¢)/š‘£^2 = ((2š‘š‘„ + š‘ž) (š‘Žš‘„ + š‘) āˆ’ a (px2 + š‘žš‘„ + š‘Ÿ) )/(ax + b)2 = (2š‘Žš‘š‘„2 + 2š‘š‘š‘„ + š‘žš‘Žš‘„ + š‘š‘ž āˆ’ š‘Žš‘š‘„2 āˆ’ š‘žš‘Žš‘„ āˆ’ š‘Žš‘Ÿ)/(ax + b)2 = (š‘Žš‘š‘„2 + 2š‘š‘š‘„ + š‘š‘ž āˆ’ š‘Žš‘Ÿ )/(ax + b)2 āˆ“ fā€™(x) = (š’‚š’‘š’™šŸ + šŸš’ƒš’‘š’™ + š’ƒš’’ āˆ’ š’‚š’“)/(š’‚š’™ + š’ƒ)šŸ

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.