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Last updated at May 29, 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) = (đđĽ2 + đđĽ + đ)/(đđĽ + đ) Let u = px2 + qx + r & v = ax + b â´ f(x) = đ˘/đŁ So, fâ(x) = (đ˘/đŁ)^â˛ fâ(x) = (đ˘^â˛ đŁ â đŁ^â˛ đ˘)/đŁ^2 Finding uâ & vâ u = px2 + qx + r uâ = p Ă 2x + q Ă 1 + 0 uâ = 2px + q v = ax + 3 vâ= a Ă 1 + 0 vâ = a fâ(x) = (đ˘/đŁ)^â˛ = (đ˘^â˛ đŁ âă đŁă^â˛ đ˘)/đŁ^2 = ((2đđĽ + đ) (đđĽ + đ) â a (px2 + đđĽ + đ) )/(ax + b)2 = (2đđđĽ2 + 2đđđĽ + đđđĽ + đđ â đđđĽ2 â đđđĽ â đđ)/(ax + b)2 = (đđđĽ2 + 2đđđĽ + đđ â đđ )/(ax + b)2 â´ fâ(x) = (đđđđ + đđđđ + đđ â đđ)/(đđ + đ)đ