Question 19 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 by

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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Question 19 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo