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

  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  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) = (𝑝π‘₯2 + π‘žπ‘₯ + π‘Ÿ)/(π‘Žπ‘₯ + 𝑏) Let u = px2 + qx + r & v = ax + b ∴ f(x) = 𝑒/𝑣 So, f’(x) = (𝑒/𝑣)^β€² f’(x) = (𝑒^β€² 𝑣 βˆ’ 𝑣^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = px2 + qx + r u’ = p Γ— 2x + q Γ— 1 + 0 u’ = 2px + q v = ax + 3 v’= a Γ— 1 + 0 v’ = a f’(x) = (𝑒/𝑣)^β€² = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = ((2𝑝π‘₯ + π‘ž) (π‘Žπ‘₯ + 𝑏) βˆ’ a (px2 + π‘žπ‘₯ + π‘Ÿ) )/(ax + b)2 = (2π‘Žπ‘π‘₯2 + 2𝑏𝑝π‘₯ + π‘žπ‘Žπ‘₯ + π‘π‘ž βˆ’ π‘Žπ‘π‘₯2 βˆ’ π‘žπ‘Žπ‘₯ βˆ’ π‘Žπ‘Ÿ)/(ax + b)2 = (π‘Žπ‘π‘₯2 + 2𝑏𝑝π‘₯ + π‘π‘ž βˆ’ π‘Žπ‘Ÿ )/(ax + b)2 ∴ f’(x) = (π’‚π’‘π’™πŸ + πŸπ’ƒπ’‘π’™ + 𝒃𝒒 βˆ’ 𝒂𝒓)/(𝒂𝒙 + 𝒃)𝟐

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.