Derivative of cosec-1 x (Cosec inverse x) - Teachoo [with Video]

Derivative of cosec-1 x (Cosec inverse x) - Part 2

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

Transcript

Derivative of ใ€–๐’„๐’๐’”๐’†๐’„ใ€—^(โˆ’๐Ÿ) ๐’™ ๐‘“ (๐‘ฅ)=ใ€–๐‘๐‘œ๐‘ ๐‘’๐‘ใ€—^(โˆ’1) ๐‘ฅ Let ๐’š= ใ€–๐’„๐’๐’”๐’†๐’„ใ€—^(โˆ’๐Ÿ) ๐’™ cosecโกใ€–๐‘ฆ=๐‘ฅใ€— ๐’™=๐œ๐จ๐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‘‘ (cosecโก๐‘ฆ ))/๐‘‘๐‘ฅ 1 = (๐‘‘ (cosecโก๐‘ฆ ))/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฆ 1 = (๐‘‘ (cosecโก๐‘ฆ ))/๐‘‘๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ 1 = โˆ’cosecโก๐‘ฆ .cotโก๐‘ฆ . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/(ใ€–โˆ’cosecใ€—โก๐‘ฆ .๐’„๐’๐’•โก๐’š ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/(ใ€–โˆ’cosecใ€—โก๐‘ฆ . โˆš(ใ€–๐œ๐จ๐’”๐’†๐’„ใ€—^๐Ÿโก๐’š โˆ’ ๐Ÿ)) Putting value of ๐‘๐‘œ๐‘ ๐‘’๐‘โก๐‘ฆ = ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (โˆ’1)/(๐‘ฅ โˆš(๐‘ฅ^2 โˆ’ 1 ) ) Hence ๐’…(ใ€–๐’„๐’๐’”๐’†๐’„ใ€—^(โ€“๐Ÿ) ๐’™)/๐’…๐’™ = (โˆ’๐Ÿ)/(๐’™ โˆš(๐’™^๐Ÿ โˆ’ ๐Ÿ ) ) As cot2 ฮธ = cosec2 ฮธ โ€“ 1, cot ฮธ = โˆš("cosec2 ฮธ โ€“ 1" ) As ๐‘ฆ = coใ€–๐‘ ๐‘’๐‘ใ€—^(โˆ’1) ๐‘ฅ So, co๐’”๐’†๐’„โก๐’š = ๐’™

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.