Question 8 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Aug. 26, 2025 by

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Question 8 If 𝑓(π‘₯)=π‘₯tan^(βˆ’1) π‘₯, then 𝑓^β€² (1) is equal to (A) πœ‹/4βˆ’1/2 (B) πœ‹/4+1/2 (C) βˆ’πœ‹/4βˆ’1/2 (D) βˆ’πœ‹/4+1/2Given 𝑓(π‘₯)=π‘₯tan^(βˆ’1) π‘₯ Now, 𝒇^β€² (𝒙)=(π‘₯tan^(βˆ’1) π‘₯)^β€² Using product rule =(π‘₯)^β€² tan^(βˆ’1) π‘₯+π‘₯ (tan^(βˆ’1)⁑π‘₯ )^β€² =1 Γ— γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) π‘₯+π‘₯ Γ—1/(1 + π‘₯^2 ) =〖𝒕𝒂𝒏〗^(βˆ’πŸ) 𝒙+𝒙/(𝟏 + 𝒙^𝟐 ) Now, 𝒇^β€² (𝟏)=γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) (1) +1/(1 + 1^2 ) =γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) (1) +1/(1 + 1) =γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) (1) +1/2 =𝝅/πŸ’ +𝟏/𝟐 So, the correct answer is (B)

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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 15 years. He provides courses for Maths, Science and Computer Science at Teachoo