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 August 14, 2026 by Teachoo

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

Ques 18 (MCQ) - If y = log(cos e^x), then dy/dx is: [Video] - Teachoo - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

part 2 - 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 - Class 12

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Transcript

Question 18 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 Given 𝑦 = 〖log 〗⁡(cos⁡〖𝑒^𝑥 〗 ) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = 𝑑(〖log 〗⁡(cos⁡〖𝑒^𝑥 〗 ) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . 𝑑(cos⁡〖𝑒^𝑥 〗 )/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . (−sin⁡〖𝑒^𝑥 〗 ) . 𝑑(𝑒^𝑥 )/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . (−sin⁡〖𝑒^𝑥 〗 ) . 𝑒^𝑥 = (−sin⁡〖𝑒^𝑥 〗)/cos⁡〖𝑒^𝑥 〗 . 𝑒^𝑥 = −tan⁡〖𝑒^𝑥 〗 . 𝑒^𝑥 = −𝒆^𝒙 . 𝒕𝒂𝒏⁡〖𝒆^𝒙 〗 So, the correct answer is (D)

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