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 )

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)

NCERT Exemplar - MCQs

Question 19 You are here

Rolle's and Mean Value Theorem →

Chapter 5 Class 12 Continuity and Differentiability

Serial order wise

About the Author

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

Accounts Tax GST

Class 6 to 8

Class 9

Class 10

Class 11

Class 12

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 )