Example 27 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Jan. 16, 2020 by Teachoo
Transcript
Example 27 Find the derivative of f given by f (x) = tan–1 𝑥 assuming it exists. f (x) = tan–1 𝑥 Let y = tan–1 𝑥 tan𝑦 = 𝑥 ∴ 𝑥 = tan𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(𝑥))/𝑑𝑥 = (𝑑 (tan𝑦 ))/𝑑𝑥 1 = (𝑑 (tan𝑦 ))/𝑑𝑥 We need d𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (tan𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = 〖𝐬𝐞𝐜〗^𝟐 𝒚 . 𝑑𝑦/𝑑𝑥 1 = (𝟏 + 𝒕𝒂𝒏𝟐𝒚) 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/(1 + 〖𝐭𝐚𝐧〗^𝟐𝒚 ) Putting 𝑡𝑎𝑛𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = 1/(1 + 𝒙^𝟐 ) As 𝑦 = tan^(−1) 𝑥 So, tan𝑦 = 𝑥 Hence (𝒅(〖𝐭𝐚𝐧〗^(−𝟏)〖𝒙)〗)/𝒅𝒙 = 𝟏/(𝟏 + 𝒙^𝟐 )
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.