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Miscellaneous (Term 1 and Term 2)
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