Miscellaneous

Chapter 12 Class 11 Limits and Derivatives
Serial order wise

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### 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﷯

#### 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.