# Misc 9 - Chapter 13 Class 11 Limits and Derivatives

Last updated at Jan. 11, 2019 by Teachoo

Last updated at Jan. 11, 2019 by Teachoo

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 + rax + b Let f(x) = px2 + qx + rax + b Let u = px2 + qx + r & v = ax + b ∴ f(x) = 𝑢𝑣 So, f’(x) = 𝑢𝑣′ f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = px2 + qx + r u’ = p . 2 .x2 – 1 + q . 1 + 0 u’ = 2px + q v = ax + 3 v’= a. 1 + 0 v’ = a f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = 2𝑝𝑥 + 𝑞 𝑎𝑥 + 𝑏 − a px2 + 𝑞𝑥 + 𝑟 ax + b2 = 2𝑎𝑝𝑥2 + 2𝑏𝑝𝑥 + 𝑞𝑎𝑥 + 𝑏𝑞 − 𝑎𝑝𝑥2 − 𝑞𝑎𝑥 − 𝑎𝑟 ax + b2 = 𝑎𝑝𝑥2 + 2𝑏𝑝𝑥 + 𝑏𝑞 − 𝑎𝑟 + 0 ax + b2 ∴ f’(x) = 𝒂𝒑𝒙𝟐 + 𝟐𝒃𝒑𝒙 + 𝒃𝒒 − 𝒂𝒓 𝐚𝐱 + 𝒃𝟐

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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.