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)

Next: Question 20 → Ask a doubt

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular

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 )

Transcript

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 )