Question 21 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by

The derivative of cos –1 (2x 2 – 1) w.r.t. cos –1 x is

(A) 2 

(B) (-1)/(2√(1-x 2 ))

(C) 2/x 

(D) 1 − x 2

This question is similar to Question 24 - CBSE Class 12 - Sample Paper for 2022 Boards

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Question 21 The derivative of cos–1 (2x2 – 1) w.r.t. cos–1x is (A) 2 (B) (−1)/(2√(1−𝑥^2 )) (C) 2/𝑥 (D) 1 − x2 Let 𝑦=〖𝑐𝑜𝑠〗^(−1)⁡𝑥 cos⁡〖𝑦=𝑥〗 〖𝒙=𝒄𝒐𝒔〗⁡𝒚 We need to find derivative of 〖𝑐𝑜𝑠〗^(−1)⁡〖(2𝑥−1)〗 w.r.t. 〖𝑐𝑜𝑠〗^(−1)⁡𝑥 i.e., 〖𝒄𝒐𝒔〗^(−𝟏)⁡〖(𝟐𝒙−𝟏)〗 w.r.t. 𝒚 i.e., (𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗⁡〖(𝟐𝒙−𝟏)〗))/𝒅𝒚 Finding (𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗⁡〖(𝟐𝒙^𝟐 − 𝟏)〗))/𝒅𝒚 (𝒅 〖(〖𝒄𝒐𝒔〗^(−𝟏)〗⁡〖(𝟐𝒙^𝟐 − 𝟏)〗))/𝒅𝒚 Putting 〖𝒙=𝒄𝒐𝒔〗⁡𝒚 = (𝑑 〖(〖𝑐𝑜𝑠〗^(−1)〗⁡〖(2 〖𝒄𝒐𝒔〗^𝟐⁡𝒚 − 1)〗))/𝑑𝑦 Using 𝒄𝒐𝒔⁡〖𝟐𝜽=𝟐〖𝒄𝒐𝒔〗^𝟐 𝜽−𝟏〗 =(𝑑 〖(〖𝑐𝑜𝑠〗^(−1)〗⁡〖(𝐜𝐨𝐬⁡𝟐𝒚)〗))/𝑑𝑦 =(𝑑(2𝑦))/𝑑𝑦 =𝟐 So, the correct answer is (A)

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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