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 August 14, 2026 by Teachoo

[MCQ] If 𝑓(𝑥)=𝑥tan^(−1) 𝑥, then 𝑓^′ (1) is equal to (A) 𝜋/4−1/2 - CBSE Class 12 Sample Paper for 2026 Boards

part 2 - Question 8 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Question 8 If 𝑓(𝑥)=𝑥tan^(−1) 𝑥, then 𝑓^′ (1) is equal to (A) 𝜋/4−1/2 (B) 𝜋/4+1/2 (C) −𝜋/4−1/2 (D) −𝜋/4+1/2Given 𝑓(𝑥)=𝑥tan^(−1) 𝑥 Now, 𝒇^′ (𝒙)=(𝑥tan^(−1) 𝑥)^′ Using product rule =(𝑥)^′ tan^(−1) 𝑥+𝑥 (tan^(−1)⁡𝑥 )^′ =1 × 〖𝑡𝑎𝑛〗^(−1) 𝑥+𝑥 ×1/(1 + 𝑥^2 ) =〖𝒕𝒂𝒏〗^(−𝟏) 𝒙+𝒙/(𝟏 + 𝒙^𝟐 ) Now, 𝒇^′ (𝟏)=〖𝑡𝑎𝑛〗^(−1) (1) +1/(1 + 1^2 ) =〖𝑡𝑎𝑛〗^(−1) (1) +1/(1 + 1) =〖𝑡𝑎𝑛〗^(−1) (1) +1/2 =𝝅/𝟒 +𝟏/𝟐 So, the correct answer is (B)

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