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Last updated at March 22, 2023 by Teachoo

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 + r)/(ax + b) Let f(x) = (ππ₯2 + ππ₯ + π)/(ππ₯ + π) Let u = px2 + qx + r & v = ax + b β΄ f(x) = π’/π£ So, fβ(x) = (π’/π£)^β² fβ(x) = (π’^β² π£ β π£^β² π’)/π£^2 Finding uβ & vβ u = px2 + qx + r uβ = p Γ 2x + q Γ 1 + 0 uβ = 2px + q v = ax + 3 vβ= a Γ 1 + 0 vβ = a fβ(x) = (π’/π£)^β² = (π’^β² π£ βγ π£γ^β² π’)/π£^2 = ((2ππ₯ + π) (ππ₯ + π) β a (px2 + ππ₯ + π) )/(ax + b)2 = (2πππ₯2 + 2πππ₯ + πππ₯ + ππ β πππ₯2 β πππ₯ β ππ)/(ax + b)2 = (πππ₯2 + 2πππ₯ + ππ β ππ )/(ax + b)2 β΄ fβ(x) = (ππππ + ππππ + ππ β ππ)/(ππ + π)π