Derivative of sec-1 x (Sec inverse x) - Teachoo [with Video]

Derivative of sec-1 x (Sec inverse x) - Part 2

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Concept wise

Transcript

Derivative of ใ€–๐’”๐’†๐’„ใ€—^(โˆ’๐Ÿ) ๐’™ ๐‘“ (๐‘ฅ)=ใ€–๐‘ ๐‘’๐‘ใ€—^(โˆ’1) ๐‘ฅ Let ๐’š= ใ€–๐’”๐’†๐’„ใ€—^(โˆ’๐Ÿ) ๐’™ secโกใ€–๐‘ฆ=๐‘ฅใ€— ๐’™=๐ฌ๐ž๐œโกใ€–๐’š ใ€— Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘๐‘ฅ/๐‘‘๐‘ฅ = (๐‘‘ (secโก๐‘ฆ ))/๐‘‘๐‘ฅ 1 = (๐‘‘ (secโก๐‘ฆ ))/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฆ 1 = (๐‘‘ (secโก๐‘ฆ ))/๐‘‘๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ 1 = ๐’•๐’‚๐’โก๐’š .๐’”๐’†๐’„โก๐’š. ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/(๐’•๐’‚๐’โก๐’š .ใ€– secใ€—โก๐‘ฆ ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/((โˆš(ใ€–๐ฌ๐ž๐œใ€—^๐Ÿโก๐’š โˆ’ ๐Ÿ)) .ใ€– secใ€—โก๐‘ฆ ) Putting value of ๐‘ ๐‘’๐‘โก๐‘ฆ = ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/((โˆš(๐‘ฅ^2 โˆ’ 1 ) ) . ๐‘ฅ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/(๐‘ฅ โˆš(๐‘ฅ^2 โˆ’ 1 ) ) Hence ๐’…(ใ€–๐’”๐’†๐’„ใ€—^(โ€“๐Ÿ) ๐’™)/๐’…๐’™ = ๐Ÿ/(๐’™ โˆš(๐’™^๐Ÿ โˆ’ ๐Ÿ ) ) As tan2 ฮธ = sec2 ฮธ โ€“ 1, tan ฮธ = โˆš("sec2 ฮธ โ€“ 1" ) As ๐‘ฆ = ใ€–๐‘ ๐‘’๐‘ใ€—^(โˆ’1) ๐‘ฅ So, ๐’”๐’†๐’„โก๐’š = ๐’™

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.