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Miscellaneous (Term 1 and Term 2)
Misc 1 (ii) Important
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Miscellaneous (Term 1 and Term 2)
Last updated at May 29, 2018 by Teachoo
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): 1ax2 + bx + c Let f(x) = 1ax2 + bx + c Let u = 1 & v = ax2 +bx+c ∴ f(x) = 𝑢𝑣 So, f’(x) = 𝑢𝑣′ f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = 1 u’ = 0 v = ax2 + bx + c v’ = a. 2x2 – 1 + b+ 0 = 2ax1 + b = 2ax + b f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = 0 𝑎𝑥2 + 𝑏𝑥 + 𝑐 − 2𝑎x + 𝑏 (1) ax2+ bc + c2 = 0 𝑎𝑥2 + 𝑏𝑥 + 𝑐 − 2𝑎x + 𝑏 (1) ax2+ bc + c2 = 0 − (2ax + b) ax2+ bc + c2 = − (2𝑎𝑥 + 𝑏) ax2+ bc + c2 Hence, f’ (x) = − (𝟐𝒂𝒙 + 𝒃) 𝐚𝐱𝟐+ 𝐛𝐜 + 𝒄𝟐