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Misc 7 - Find derivative: 1/ ax2 + bx + c - Chapter 13 NCERT - Derivatives by formula - x^n formula

Misc 7 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Misc 7 - Chapter 13 Class 11 Limits and Derivatives - Part 3


Transcript

Misc 7 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): 1﷮ax2 + bx + c﷯ Let f(x) = 1﷮ax2 + bx + c﷯ Let u = 1 & v = ax2 +bx+c ∴ f(x) = 𝑢﷮𝑣﷯ So, f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ f’(x) = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ Finding u’ & v’ u = 1 u’ = 0 v = ax2 + bx + c v’ = a. 2x2 – 1 + b+ 0 = 2ax1 + b = 2ax + b f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ = 0 𝑎𝑥2 + 𝑏𝑥 + 𝑐 ﷯ − 2𝑎x + 𝑏﷯ (1) ﷮ ax2+ bc + c﷯2﷯ = 0 𝑎𝑥2 + 𝑏𝑥 + 𝑐 ﷯ − 2𝑎x + 𝑏﷯ (1) ﷮ ax2+ bc + c﷯2﷯ = 0 − (2ax + b)﷮ ax2+ bc + c﷯2﷯ = − (2𝑎𝑥 + 𝑏)﷮ ax2+ bc + c﷯2﷯ Hence, f’ (x) = − (𝟐𝒂𝒙 + 𝒃)﷮ 𝐚𝐱𝟐+ 𝐛𝐜 + 𝒄﷯𝟐﷯

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.