CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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Question 18 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

If y = log⁡(cos⁡ e x ), then dy/dx is :

(a) cose (x-1)   (b) e (-x) cos e x
(c) e x sine x    (d) -e x tan e x

 

This question is inspired from Ex 5.4, 5 - Chapter 5 Class 12 - Continuity and Differentiability

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Transcript

Question 18 If y = ๐‘™๐‘œ๐‘”โก(๐‘๐‘œ๐‘ โกใ€–๐‘’^๐‘ฅ ใ€— ), then ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ is : (a) ๐‘๐‘œ๐‘ ๐‘’^(๐‘ฅโˆ’1) (b) ๐‘’^(โˆ’๐‘ฅ) "cos" ๐‘’^๐‘ฅ (c) ๐‘’^๐‘ฅ ๐‘ ๐‘–๐‘›๐‘’^๐‘ฅ (d) ใ€–โˆ’๐‘’ใ€—^๐‘ฅ " tan" ใ€– ๐‘’ใ€—^๐‘ฅ Given ๐‘ฆ = ใ€–log ใ€—โก(cosโกใ€–๐‘’^๐‘ฅ ใ€— ) Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ = ๐‘‘(ใ€–log ใ€—โก(cosโกใ€–๐‘’^๐‘ฅ ใ€— ) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/cosโกใ€–๐‘’^๐‘ฅ ใ€— . ๐‘‘(cosโกใ€–๐‘’^๐‘ฅ ใ€— )/๐‘‘๐‘ฅ = 1/cosโกใ€–๐‘’^๐‘ฅ ใ€— . (โˆ’sinโกใ€–๐‘’^๐‘ฅ ใ€— ) . ๐‘‘(๐‘’^๐‘ฅ )/๐‘‘๐‘ฅ = 1/cosโกใ€–๐‘’^๐‘ฅ ใ€— . (โˆ’sinโกใ€–๐‘’^๐‘ฅ ใ€— ) . ๐‘’^๐‘ฅ = (โˆ’sinโกใ€–๐‘’^๐‘ฅ ใ€—)/cosโกใ€–๐‘’^๐‘ฅ ใ€— . ๐‘’^๐‘ฅ = โˆ’tanโกใ€–๐‘’^๐‘ฅ ใ€— . ๐‘’^๐‘ฅ = โˆ’๐’†^๐’™ . ๐’•๐’‚๐’โกใ€–๐’†^๐’™ ใ€— So, the correct answer is (D)

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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.