If  y = log ((1 - x 2 )/(1 + x 2 )),then dy/dx is equal to

(A) ใ€–4x 3 /(1-x 4

(B) (-4x)/(1-x 4 )

(C) 1/(4-x 4

(D) (-4x 3 )/(1-x 4 )

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

Transcript

Question 21 If y = log ((1 โˆ’ ๐‘ฅ^2)/(1 + ๐‘ฅ^2 )),then ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ is equal to (A) ใ€–4๐‘ฅใ€—^3/(1โˆ’๐‘ฅ^4 ) (B) (โˆ’4๐‘ฅ)/(1โˆ’๐‘ฅ^4 ) (C) 1/(4โˆ’๐‘ฅ^4 ) (D) (โˆ’4๐‘ฅ^3)/(1โˆ’๐‘ฅ^4 ) y=log((1 โˆ’ ๐‘ฅ^2)/(1 +ใ€– ๐‘ฅใ€—^2 )) ๐ฒ=๐ฅ๐จ๐ (๐Ÿโˆ’๐’™^๐Ÿ )โˆ’๐ฅ๐จ๐ โกใ€–(๐Ÿ+๐’™^๐Ÿ)ใ€— Differentiating wrt ๐‘ฅ ๐’…๐’š/๐’…๐’™=๐‘‘(log(1 โˆ’ ๐‘ฅ^2 ) โˆ’ logโกใ€–(1 + ๐‘ฅ^2)ใ€— )/๐‘‘๐‘ฅ =๐‘‘(log(1 โˆ’ ๐‘ฅ^2 ))/๐‘‘๐‘ฅโˆ’๐‘‘(log(1 + ๐‘ฅ^2 ))/๐‘‘๐‘ฅ =๐Ÿ/((๐Ÿ โˆ’ ๐’™^๐Ÿ ) ) ๐’…(๐Ÿ โˆ’ ๐’™^๐Ÿ )/๐’…๐’™โˆ’๐Ÿ/((๐Ÿ + ๐’™^๐Ÿ ) ) ๐’…(๐Ÿ + ๐’™^๐Ÿ )/๐’…๐’™ =1/((1 โˆ’ ๐‘ฅ^2 ) )(0โˆ’2๐‘ฅ)โˆ’1/((1 + ๐‘ฅ^2 ) ) (0+2๐‘ฅ) =(โˆ’2๐‘ฅ)/((1 โˆ’ ๐‘ฅ^2 ) )โˆ’2๐‘ฅ/((1 + ๐‘ฅ^2 ) ) =โˆ’2๐‘ฅ(1/((1 โˆ’ใ€– ๐‘ฅใ€—^2 ) )+1/((1 +ใ€– ๐‘ฅใ€—^2 ) )) =โˆ’2๐‘ฅ((1 + ๐‘ฅ^2 + 1 โˆ’ใ€– ๐‘ฅใ€—^2)/(1 โˆ’ ๐‘ฅ^2 )(1 + ๐‘ฅ^2 ) ) =โˆ’2๐‘ฅ(2/(1 โˆ’ใ€– ๐‘ฅใ€—^2 )(1 + ๐‘ฅ^2 ) ) =(โˆ’๐Ÿ’๐’™)/(๐Ÿ โˆ’ ๐’™^๐Ÿ’ ) So, the correct answer is (B)

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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.