Check sibling questions

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

(A) γ€–4x 3 /(1-x 4 )Β 

(B) (-4x)/(1-x 4 )

(C) 1/(4-x 4 )Β 

(D) (-4x 3 )/(1-x 4 )

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Transcript

Question 21 If y = log ((1 βˆ’ π‘₯^2)/(1 + π‘₯^2 )),then 𝑑𝑦/𝑑π‘₯ is equal to (A) γ€–4π‘₯γ€—^3/(1βˆ’π‘₯^4 ) (B) (βˆ’4π‘₯)/(1βˆ’π‘₯^4 ) (C) 1/(4βˆ’π‘₯^4 ) (D) (βˆ’4π‘₯^3)/(1βˆ’π‘₯^4 ) y=log((1 βˆ’ π‘₯^2)/(1 +γ€– π‘₯γ€—^2 )) 𝐲=π₯𝐨𝐠(πŸβˆ’π’™^𝟐 )βˆ’π₯𝐨𝐠⁑〖(𝟏+𝒙^𝟐)γ€— Differentiating wrt π‘₯ π’…π’š/𝒅𝒙=𝑑(log(1 βˆ’ π‘₯^2 ) βˆ’ log⁑〖(1 + π‘₯^2)γ€— )/𝑑π‘₯ =𝑑(log(1 βˆ’ π‘₯^2 ))/𝑑π‘₯βˆ’π‘‘(log(1 + π‘₯^2 ))/𝑑π‘₯ =𝟏/((𝟏 βˆ’ 𝒙^𝟐 ) ) 𝒅(𝟏 βˆ’ 𝒙^𝟐 )/π’…π’™βˆ’πŸ/((𝟏 + 𝒙^𝟐 ) ) 𝒅(𝟏 + 𝒙^𝟐 )/𝒅𝒙 =1/((1 βˆ’ π‘₯^2 ) )(0βˆ’2π‘₯)βˆ’1/((1 + π‘₯^2 ) ) (0+2π‘₯) =(βˆ’2π‘₯)/((1 βˆ’ π‘₯^2 ) )βˆ’2π‘₯/((1 + π‘₯^2 ) ) =βˆ’2π‘₯(1/((1 βˆ’γ€– π‘₯γ€—^2 ) )+1/((1 +γ€– π‘₯γ€—^2 ) )) =βˆ’2π‘₯((1 + π‘₯^2 + 1 βˆ’γ€– π‘₯γ€—^2)/(1 βˆ’ π‘₯^2 )(1 + π‘₯^2 ) ) =βˆ’2π‘₯(2/(1 βˆ’γ€– π‘₯γ€—^2 )(1 + π‘₯^2 ) ) =(βˆ’πŸ’π’™)/(𝟏 βˆ’ 𝒙^πŸ’ ) So, the correct answer is (B)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.