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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise

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 + 1/๐‘ฅ)/(1 โˆ’ 1/๐‘ฅ) Let f(x) = (1 + 1/๐‘ฅ)/(1 โˆ’ 1/๐‘ฅ) = ((x + 1)/x)/((x โˆ’ 1)/x) = (x + 1)/x ร— ๐‘ฅ/(๐‘ฅ โˆ’ 1) = (๐‘ฅ + 1)/(๐‘ฅ โˆ’ 1 ) So, f(x) = (๐‘ฅ + 1)/(๐‘ฅ โˆ’ 1 ) โˆด f(x) = ๐‘ข/๐‘ฃ So, fโ€™(x) = (๐‘ข/๐‘ฃ)^โ€ฒ = (u^โ€ฒ v โˆ’ v^โ€ฒ u)/v^2 Now, u = x + 1 uโ€™ = 1 + 0 = 1 v = x โ€“ 1 vโ€™ = 1 โ€“ 0 = 1 Now, fโ€™(x) = (๐‘ข/๐‘ฃ)^โ€ฒ = (๐‘ข^โ€ฒ ๐‘ฃ โˆ’ใ€– ๐‘ฃใ€—^โ€ฒ ๐‘ข)/๐‘ฃ^2 = (1 (x โˆ’ 1) โˆ’1 (x + 1) )/(x โˆ’ 1)^2 = (x โˆ’ 1 โˆ’ x โˆ’ 1)/(x โˆ’ 1)^2 = (โˆ’ 2)/(x โˆ’ 1)^2 Hence, fโ€™ (x) = (โˆ’ ๐Ÿ)/(๐ฑ โˆ’ ๐Ÿ)^๐Ÿ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.