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

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

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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’™

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.