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Last updated at Nov. 30, 2019 by Teachoo

Misc 6 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): (1 + 1/π₯)/(1 β 1/π₯) Let f(x) = (1 + 1/π₯)/(1 β 1/π₯) = ((x + 1)/x)/((x β 1)/x) = (x + 1)/x Γ π₯/(π₯ β 1) = (π₯ + 1)/(π₯ β 1 ) So, f(x) = (π₯ + 1)/(π₯ β 1 ) β΄ f(x) = π’/π£ So, fβ(x) = (π’/π£)^β² = (u^β² v β v^β² u)/v^2 Now, u = x + 1 uβ = 1 + 0 = 1 v = x β 1 vβ = 1 β 0 = 1 Now, fβ(x) = (π’/π£)^β² = (π’^β² π£ βγ π£γ^β² π’)/π£^2 = (1 (x β 1) β1 (x + 1) )/(x β 1)^2 = (x β 1 β x β 1)/(x β 1)^2 = (β 2)/(x β 1)^2 Hence, fβ (x) = (β π)/(π± β π)^π