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Chapter 5 Class 12 Continuity and Differentiability

Serial order wise

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

Last updated at Dec. 16, 2024 by Teachoo

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 )

[MCQ] If y = log ((1 − 𝑥^2)/(1 + 𝑥^2 )), then 𝑑𝑦/𝑑𝑥 is equal to - NCERT Exemplar - MCQs

part 2 - Question 19 - NCERT Exemplar - MCQs - Serial order wise - Chapter 5 Class 12 Continuity and Differentiability

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Transcript

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

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

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