Misc 6 - Chapter 13 Class 11 Limits and Derivatives
Last updated at Nov. 30, 2019 by Teachoo
Last updated at Nov. 30, 2019 by Teachoo
Transcript
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 + 1/๐ฅ)/(1 โ 1/๐ฅ) Let f(x) = (1 + 1/๐ฅ)/(1 โ 1/๐ฅ) = ((x + 1)/x)/((x โ 1)/x) = (x + 1)/x ร ๐ฅ/(๐ฅ โ 1) = (๐ฅ + 1)/(๐ฅ โ 1 ) So, f(x) = (๐ฅ + 1)/(๐ฅ โ 1 ) โด f(x) = ๐ข/๐ฃ So, fโ(x) = (๐ข/๐ฃ)^โฒ = (u^โฒ v โ v^โฒ u)/v^2 Now, u = x + 1 uโ = 1 + 0 = 1 v = x โ 1 vโ = 1 โ 0 = 1 Now, fโ(x) = (๐ข/๐ฃ)^โฒ = (๐ข^โฒ ๐ฃ โใ ๐ฃใ^โฒ ๐ข)/๐ฃ^2 = (1 (x โ 1) โ1 (x + 1) )/(x โ 1)^2 = (x โ 1 โ x โ 1)/(x โ 1)^2 = (โ 2)/(x โ 1)^2 Hence, fโ (x) = (โ ๐)/(๐ฑ โ ๐)^๐
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