Misc 5 - Class 11

Last updated at May 29, 2018 by Teachoo

Misc 5 - Find derivative: ax + b / cx + d - Chapter 13 Class 11 - Miscellaneous

Transcript

Misc 5 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): 𝑎𝑥 + 𝑏﷮𝑐𝑥 + 𝑑﷯ Let f(x) = 𝑎𝑥 + 𝑏﷮𝑐𝑥 + 𝑑﷯ Let u = ax + b & v = cx + d ∴ f(x) = 𝑢﷮𝑣﷯ So, f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ f’(x) = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ Finding u & v u = ax + b u’ = a + 0 = a v = cx + d v’ = c + 0 = c f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ = 𝑎 𝑐𝑥 + 𝑑﷯ − 𝑐 (𝑎𝑥 + 𝑏)﷮ 𝑐x + d﷯2﷯ = acx + ad − 𝑎𝑐𝑥 − 𝑐𝑏﷮ cx + 𝑑﷯2﷯ = acx + ad − 𝑎𝑐𝑥 − 𝑐𝑏﷮ cx + 𝑑﷯2﷯ = ad − cb﷮ cx + 𝑑﷯2﷯ Hence, f’ (x) = 𝐚𝐝 − 𝒄𝒃﷮ 𝐜𝐱 + 𝒅﷯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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.