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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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) = (𝑝𝑥2 + 𝑞𝑥 + 𝑟)/(𝑎𝑥 + 𝑏) Let u = px2 + qx + r & v = ax + b ∴ f(x) = 𝑢/𝑣 So, f’(x) = (𝑢/𝑣)^′ f’(x) = (𝑢^′ 𝑣 − 𝑣^′ 𝑢)/𝑣^2 Finding u’ & v’ u = px2 + qx + r u’ = p × 2x + q × 1 + 0 u’ = 2px + q v = ax + 3 v’= a × 1 + 0 v’ = a f’(x) = (𝑢/𝑣)^′ = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 = ((2𝑝𝑥 + 𝑞) (𝑎𝑥 + 𝑏) − a (px2 + 𝑞𝑥 + 𝑟) )/(ax + b)2 = (2𝑎𝑝𝑥2 + 2𝑏𝑝𝑥 + 𝑞𝑎𝑥 + 𝑏𝑞 − 𝑎𝑝𝑥2 − 𝑞𝑎𝑥 − 𝑎𝑟)/(ax + b)2 = (𝑎𝑝𝑥2 + 2𝑏𝑝𝑥 + 𝑏𝑞 − 𝑎𝑟 )/(ax + b)2 ∴ f’(x) = (𝒂𝒑𝒙𝟐 + 𝟐𝒃𝒑𝒙 + 𝒃𝒒 − 𝒂𝒓)/(𝒂𝒙 + 𝒃)𝟐

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.