Question 19 If y = log ((1 − 𝑥^2)/(1 + 𝑥^2 )),then 𝑑𝑦/𝑑𝑥 is equal to (A) 〖4𝑥〗^3/(1−𝑥^4 ) (B) (−4𝑥)/(1−𝑥^4 ) (C) 1/(4−𝑥^4 ) (D) (−4𝑥^3)/(1−𝑥^4 ) y=log((1 − 𝑥^2)/(1 +〖 𝑥〗^2 )) 𝐲=𝐥𝐨𝐠(𝟏−𝒙^𝟐 )−𝐥𝐨𝐠⁡〖(𝟏+𝒙^𝟐)〗 Differentiating wrt 𝑥 𝒅𝒚/𝒅𝒙=𝑑(log(1 − 𝑥^2 ) − log⁡〖(1 + 𝑥^2)〗 )/𝑑𝑥 =𝑑(log(1 − 𝑥^2 ))/𝑑𝑥−𝑑(log(1 + 𝑥^2 ))/𝑑𝑥 =𝟏/((𝟏 − 𝒙^𝟐 ) ) 𝒅(𝟏 − 𝒙^𝟐 )/𝒅𝒙−𝟏/((𝟏 + 𝒙^𝟐 ) ) 𝒅(𝟏 + 𝒙^𝟐 )/𝒅𝒙 =1/((1 − 𝑥^2 ) )(0−2𝑥)−1/((1 + 𝑥^2 ) ) (0+2𝑥) =(−2𝑥)/((1 − 𝑥^2 ) )−2𝑥/((1 + 𝑥^2 ) ) =−2𝑥(1/((1 −〖 𝑥〗^2 ) )+1/((1 +〖 𝑥〗^2 ) )) =−2𝑥((1 + 𝑥^2 + 1 −〖 𝑥〗^2)/(1 − 𝑥^2 )(1 + 𝑥^2 ) ) =−2𝑥(2/(1 −〖 𝑥〗^2 )(1 + 𝑥^2 ) ) =(−𝟒𝒙)/(𝟏 − 𝒙^𝟒 ) 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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

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

(A) 〖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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Davneet Singh

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

(A) 〖4x ³ /(1-x ⁴ )

(B) (-4x)/(1-x ⁴ )

(C) 1/(4-x ⁴ )

(D) (-4x ³ )/(1-x ⁴ )