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Last updated at Nov. 30, 2019 by Teachoo

Misc 28 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): π₯/(1 + π‘ππβ‘π₯ ) Let f (x) = π₯/(1 + π‘ππβ‘π₯ ) Let u = x & v = 1 + tan x So, f(x) = π’/π£ β΄ fβ(x) = (π’/π£)^β² Using quotient rule fβ(x) = (π’^β² π£ βγ π£γ^β² π’)/π£^2 Finding uβ & vβ u = x uβ = 1 & v = 1 + tan x vβ = (1 + tan x)β = 0 + sec2 x = sec2 x Now, fβ(x) = (π’/π£)^β² = (π’^β² π£ βγ π£γ^β² π’)/π£^2 = (1(1 +γ tanγβ‘γπ₯)γ β π ππ2 π₯ (π₯))/γ(1 +γ tanγβ‘γπ₯)γγ^2 = (π +γ πππγβ‘γπ β π ππππ πγ)/γ(π +γ πππγβ‘γπ)γγ^π = (π’^β² π£ βγ π£γ^β² π’)/π£^2 = (1(1 +γ tanγβ‘γπ₯)γ β π ππ2 π₯ (π₯))/γ(1 +γ tanγβ‘γπ₯)γγ^2 = (π +γ πππγβ‘γπ β π ππππ πγ)/γ(π +γ πππγβ‘γπ)γγ^π